MASTER 

NEGA  TIVE 
NO.  93-81223 


MICROFILMED  1993 
COLUMBIA  UNIVERSITY  LIBRARIES/NEW  YORK 


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AUTHOR: 


STINSON,  JOHN  H. 


TITLE: 


ORGANON  OF  SCIENCE 


PLACE: 


EUREKA,  CALIF 


DA  TE : 


1879 


COLUMBIA  UNIVERSITY  LIBRARIES 
PRESERVATION  DEPARTMENT 

t 

BIBLIOGRAPHIC  MTCRnFORM  TARHFT 


Master  Negative  # 


Restrictions  on  Use: 


Original  Material  as  Filmed  -  Existing  Bibliographic  Record 


108 
Z3 
V.2 


Stinson,  John  Harrison.    1330-  isoo . 

Orgaiioii  of  science.  Three  books  in  one  volume,  by 
Jolin  Ilarnson  Stinson  ...  Eureka,  Cal.,  W.  Ayres, 
printer,  18/9.  -  *^      ' 

115,  35,  43  p.    diagrs.     I7i'"^.in    25f,  en. 
Voli:no   of  panphlct'j. 


I.  Philosophy— Miscellanea. 


11-24661 


Library  of  Congress 
Copyright    1871 :  6466 


(•      I    BD701.S8 


^t 


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ORGANOISr  OF  SCIENCE 


-H)+ 


Thi*ee  Books  In  One  Tolnme, 


BY 


y     JOHLT^    HTA^lEfclCrROISr    QTETlSr^OlS^,    Eeq^. 


-HH- 


-•-♦«€»•+—• 


'  Omnibus  has   Literas  peTlecfihrls   Salutem!'^ 


M-H 


EUREKA,  CALIFORNIA: 

Wm.  ayres,  book  and  job  printer, 

107  FIRST   STREET, 
1879. 


■  ^1  *W     '^fm—  ~  ■ 


Entered  according  to  Act  of  Congress  in  the  year  A.  D.  1871,  by 

JOHN  HARRISON  STINSON,  Esq., 

In  the  office  of    the  Librarian  of    Congress  at  Washington,  D.  C. 


f 


PBEFACE. 

:o: 

In  offering  a  new  system  of   philosophy   to   the  scientific   world   the 
author  is  :.wMre  thnt  mrt:..v  wll  s^v  of  it  at  iv  ontset  as  Omer  Pasha  did  of 
the  Alexandrian  Library,  "If  it  contain  the  Koran,  we  have  it  already  and 
whatever  el.e  ii  may  contain  's  not  worth  having."     We  can  only  remind  such 
persons  that  the  present  age  is  one  of  free  inquiry,  that  the  human  mind  at 
best  IS  very  feeble  and  easily  deceived  by  appearances,  and  that  though  we 
may  be  contented  and  cntirmed  in  our  opinions,  which  are  support^ed  by 
the  names  of  distinguished  philosophers;  yet  our  condition,  perhaps  may  be 
no  more  happy  than  that  of  Pollock's  rustic,  who  was  confirmed  in  the  belief 
liiat  the  v:«nrd   line  which  i  irt  him  rour.d   f.bont   wns  the  world's  extreme 
Fortunately  for  the  hum.in  race,  however,  there  is  a  class  of  men  in  America 
and  Europe,  whose  reflections  leach  them,  that  there  can  be  no  great  advance 
HI  civilization  without  an  increase  of  knowledge  in  science.    To  such  persons 
Iheaulhor  must   look  for  a  fair  examination  of  tlje  present  work.     And   in 
calling  the  attention  r,t  seekers  after  scientific  truth  in  a  pref^pe,  lillle  more 
can  be  done  by  an  author  than   to  promise  that,  in  the  author's  opinion,  a 
thorough  perusal  will  repay  ihe  reader. 

The  flKuighfs  co:.faiued  in  this  book  hnvo  been  rainvd  bv  mucli  labor 
and  have  not  been  set  down  without  much  lefieclion.  The  subject  is  a  pro- 
lound  one:  and  it  is.  indeed,  fo  the  matured  philosopher,  whose  mind  has 
been  grappling  witli  intricate  scientific  questions,  and  who  can  command  and 
concentrate  his  thonght.s,  thai,  in  the  first  instance,  the  value  of  new  scientific 
irnlhs  must  be  perceived  and  appreciaterl.  To  such  matured  minds  wo  say; 
read  our  book  carelull'-,  and  speak  your  minds  In  ely  respecting  its  merit.s! 
For  we  believe,thai  the  philosophic  seeker  for  truth,  of  the  present  and  future 
ages,  will  find  in  it  sumdcni  im:nulriMc  and  valnahle  truth  to  approve  and 
justEfy  the  lime  and  labor  spent  by  ilie  author  in  his  attempt  to  correct  errors 
and>t(»  open  the  gales  of  sei«  jitific  truth  to  mankind.  The  Author. 

Eureka,  CaliforniH.  .Janu.irv  2r».  IS79. 


■  -w     ■^.j'-.ji.'-aJAi.-iJ 


1  XTR  OB  UC  TIOX. 


K 


Philosopliy  and  theinlt-IIectual  sciences  like  statues/' sa3^ri  Bacon, 


(I 


are 


ndorncd  and  ceUbraled,  bnt  are  nol  made  to  advance;  nay,  they  are  frequently 


vi«;:(>n)us  in  the  hand*  of  their  author,  and  thencefor 


nmark  of  Bacon's  is  iitferaliv  true  of    Locic;    which 


ward  tlegenerate."     This 


BUj^iiest  t«)  tiie  reader   that  diss  of  studies  at  the  present  ( 

related  than  any  rMher  to  the  suhjfvt  matter  of  thi^  hook.    And  in  altmipt 


word   Mill    piobnbly 
ime   more   nearly 


to  explain   somethinj^  new  and   unknr>wn   to  the   read 


int; 


er,   we   are  frerjueully- 


ohliged  to  make  ourselves  undjTstood  hy  rcferjuce  to  somelhinc  already' 
known,  [n  our  introdrction  of  tjie  reader  to  the  explanations  and  substances 
of  the  science  which  we  have  endeavored  to  exhibit  in  the  subsequent  oaj^es, 
therefore,  we  W(  uld  ask  and  expect  that  he  has  some  knowledsrcof  il»e  stand- 
ard works  upon  logic,  among  which  that  of  Arehbislu  p  Whateir  is  as  able  a 
specimen  <d  the  reeeivtd  systenu  as  any;  and  as  it  is  condense  and  contains 


but   liltie  irrelevent  matter,  it   is  therefore  to  l)e  preferred   t 


n  i\u\  other.     We 


may  :  e   in 


k\o  not,  however,  insist  that  the  followinir  pM<r<'s  can  not  be  understood  will 
out  such  previous  ae(ju  lintance  with  the  works  of  others.     We  have  emiejiv 
ored   to  luake   this  treatise  as  elementa;y  asjjossible;  so  that   it 
itself  sufticienl  lo  ciuivince  and  instruct  the  reader  in  its  various  dictrines- 

oj^ic   will    have 

ies  in  the  way, 

ion.     And  we  do 

considrration  of   tliis  book 


Yel  siKMi  previous  nc(|uaintanc«  with  ihe  popular  works  on   1 
brou<jht  any  (uie  to  some  appreciation  ot  some  of  Ijie  difliculi 
and  therefore  he  will   lie   better  prepared  for  Ihe  investii^al 
positi/ely  insist  that  the  readir  shall  come  to  the 


with  a  trained  mind, 


i;  On  the  other  hand   we  do  not  object   to  the  popular  systems  of   lode 

i  be(ause  that  scienct  has  n(H  in  Ihe  succeeding  a«2:es  frrmi  Aristotle,  its  author, 

|{  unravelled  ii.M-lf  into  L'^realer  number  of  detaiN,  or  varii-d  its  elementarv  prin- 

rlpks.  True  principles  are  immutable, and  to  depart  from  them  isto  M\  into 
ernu-.  But  Ihe  popular  systems  of  lon^io,  Jn  onr  estimation,  posses^j  no  value 
excrpi  in  disputj.tions;  they  are  in  fact  what  Arclibish<»p  Whatelv  saysOf 
lojic  in  ceneral,  '  Kjir-ly  conversant  about  lauiruage."  That  the  popular 
systf-ms  of    lojL'ic    make    the    analysis,  an<l  exjdain  t lie  true  processes  of  the 


mind  in  reasoninL^  we  do  not  believe,  and  therefore  We  do  not 


repird  them  as 


of    any  yalue  In  assistinir  any  )»erson  in   his  search  after  truth.     In   d 
men  by  their  own  wonis  to  admit  what  thev  already  know  to  be  t 


rivin:'' 


rue,  1.  e..  in 


argumentalion,  thev  may  beof  viIik-;  l>ut  in  making  iiderenees  from  trull 


IS 


know'n  to  trutl.9  unko.wn,  the  mind  does  not  proceeil  upon  the  principles 
"set  forth  in  the  Aristotelian  method.,  and  therefore  these  methods  arc  ol  no 
value  to  science.    In  the  language  of  Bacon  "They  force  assent  not  things. 
AUhough  the  dialects  of  Aristotle  have  been  before  the  world  tor  many  cen- 
turies yet  no  one,  however  well  acquainted  with  the  system,  has  advanced   to 
one  n;w  truth  in  science  by  the  method  therein  laid  down.    And  ,     logic  is 
not  a  peculiar  method  of  reasoning,  but  tub  method  upon  which  all  true 
re.son.n.'  proceeds,  as  contended    by   Whaley  and  others,  then  the  grea 
advance  wliich  has  been  made  in  the  sciences  must  have  been  mn»le  without 
reasoning  at  all,  or  else  the  method  of  reasoning  is  not  shell  as  it  has  becu 
stalctl  and  explained  by  those  authors. 

But  although  the  popular  systems  of  logic  are  of  no  value  in  assisting 
to  lav  the  foundations,  or  to  rear  the  superstructure  of  the  physical,  abstract 
or  mental  sciences,  yet  for  the  purposes  of  adorning  and  giving  force  to  speech 
•they  are  not  without  value.    Archbishop  Whately  regards  rhet-ric  as  the  off- 
shoot from  logic ;  in  our  estimation  all  that  is  valuable  in  the  popular  systems 
of  logic  belongs  more  properly  to  rhetoric  than  to  any  other  science     It   is 
°rue  that  whenever  we  reason  i.e.  we  make  inferences  from  truths  known  to  truths 
unknown  certain  processes  take  place  in  the  mind,  and   that   these  processes 
are  alike  in  the  minds  of  all  men  who  re,«on  correctly.    It  is  also  true  that 
the  popular  systems  of  logic  explain  with  tolerable  c.rrectness  the  manner  of 
word.n-  our  premis.-  and  conclu..ioDs  in  what  is  called  ratiocination.    And 
to  go  even  thus  far  is  an  acquisition  of  no  small  value.    But  it  is  somewhat 
stranc^e  that  writers  on  logic,  of  the  most  brilliant  talents,  who  so   requently 
warn°us  against  the  liability  of  being  imposed  upon   by  w  .rds,  should  ye 
never   have  penetrated   beneath  the  words  to  the  things   that   hav.   bronght 
aLut  these  words  with  their  manner  of   usage.     Words   are  used   in   every 
science-  but  no  science  constructed  upon  word.can  touch  the  limits  of  things 
0  ment'al  or  physical  nature.    The  processes  of  the  mind  in  reasoning    eave 
,o  sensible  trace  behind  them;  words  do  not  stand  as  sensible  signs  of    l.ese 
;;.cesscs.    The  mind  by  its  pr„cesses  forms  words  but  the  P''---  '^;- 
selvcs  are  at  the  bottom,  and  they  lie  deeper  than  the  words.     •  A  pr»p..s.- 
U<  .  "  says  Whately,  "  is  defined  logically  a  sentence  in.Ucat.ve  ..  e  afflrming 
o     deny  ng;  (this  exclu.les  commands  and  questions)  sentenck   being  the 
genus   and     ND.CAT.VE  the  difference,  this  definition   expresses  the   whole 
tZce-  and  it  relates  entirely  to  the  words  of  a  proposition."    Any  one  can 
e^"vs  ethat  the  above  definition  is  grounded  entirely   upon   gram.natical 
dtilctions,  and  as  s.at..d  by  Whately,  "It  relates  ent(My  to  the  words  of  a 

'"'"'"' T,',  make  a  scientific  analysis  and  explain  the  processes  of  the  mind  in 
rensonin"  require  a  difteren.  treatment  and  mode  of  investigation  rom  that 
X"o  pursued  by  writers  upon  Ugic.  -And  we  may  in  truth  say  that  in  the 


pagea  of  this  book,  we  have  pursued  a  method,  in  the  greater  part,  unattemp- 
ted  heretofore.  And  certainly  tlie  exigencies  ot  the  world  demand  a  better^ 
philosophy  of  reasoning  than  writers  heretofore  have  given.  If  we  look 
about  us  in  our  own  country,  or  travel  abroad  and  observe  the  various  opin- 
ions concerning  the  most  common  aflairs  and  effects,  and  notice  the  zeal  with 
which  men  pursue  the  most  absurd  theories,  we  will  conclude  with  the  great 
English  philosopher,  that  "the  specious  meditations,  speculations  and  theories 
of  mankind,  are  but  a  kind  of  insanity,  only  there  is  no  one  to  stand  by  and 
observe  it."  It  is  true  thai  m.idmen  may  agree  pretty  well  on  many  points 
and  the  grave  digger  in  the  play  thought  that  Hamlet's  madness  would  not 
be  noticed  in  England  among  a  people  as  mad  as  himself.  And  notwithstand- 
ing the  advancement  which  kas  been  made  in  the  arts,  and  many  of  the 
sciences  during  the  present  century,  men  yet  are  driven  about  in  their  opin- 
ions as  though  there  was  no  certain  truth  to  be  obtained,  or  else  they  pursue 
some  absurdity  as  though  error  and  truth  both  were  in  effect  the  same  thing. 
And  from  these  sources  of  trouble,  which  set  men  to  travel  the  wrong  road 
to  happiness  and  true  progress,  there  is  no  escape  for  mankind  except  in  the 
further  development  of  the  sciences.  But  in  the  words  of  Bacon,  "The  pres- 
ent systems  of  logic  are  useless  for  the  discovery  of  the  sciences,"  and  "they 
rather  assist  in  confirming  and  rendering  inveterate  the  errors  founded  on 
vulgar  notions  than  in  searching  after  truth." 

"The  unassisted  hand,"  however,  "and  the  understanding  left  to  itself 
posesses  but  little  power.  Effects  are  produced  by  the  means  of  instruments 
and  helps,  which  the  understanding  requires  no  less  than  the  hand."  And. in 
looking  after  helps  for  the  understanding,  we  would  naturally  inquire  by 
what  means  any  one,  who  had  madedisco^^eries  in  science,  had  been  assisted 
in  his  efforts.  If  any  one  should  see  a  mathematician  calculate  the  distance 
to  a  certain  object,  or  tell  the  highl  of  a  tree  without  measuring  it.  and  he 
find  the  result  to  be  as  the  mathematician  had  stated,  he  would  very  naturally 
inquire  how  such  knowledge  could  be  obtained;  by  what  means  could  such 
conclusions  be  reached.  And  every  one  knows  that  the  science  of  mathe- 
matics is  a  most  i>owerful  instrument  for  solving  those  problems  ©f  nature 
wliich  come  within  its  province.  But  tlie  science  of  mathematics  itself  has 
been  discovered  and  its  truths  have  been  brought  to  light  by  certain  processes 
of  the  ind  And  those  processes  of  the  mind,  which  have  brought  to  light 
some  truths  in  any  given  case,  will,  if  exercised  again  in  like  manner,  bring 
to  light  other  truths  of  a  like  nature.  The  mind  cerlamly  possesses  the 
power  to  gain  knowle(lge  by  some  method,  and  were  this  method  certainly 
known  and  cl«arly  explained,  it  could  be  used  to  advance  «ir  knowledge  in 
science,  unless  all  the  subjects  to  which  it  is  applicable  are  exhausted.  But 
the  greater  number  of  the  sciences  are  confessedly  yet  in  their  infancy,  and 
the  progress,  which   is  made  in  them^ecms  to  proceed  in  most   instances 


8 
rather  bv  nhance  Ihan  bv  any  direction  wbirh  plnN-.^plior^  have  ur/en.    Tbe 
scbool-boy  al  the  pifsent  day  stiulies  his  loi^ic;  but  tl-e  man  who  goos  forlh 
in  the  ficarch  ot    truth,  throws  it  away  expecting  no   hrlp  from  it.    Thos« 
men    who  have  advanced  science  the  most,  have  paid   but  liltle   r«gaj-d  to 
those  phib)Hlphers  who  have  treated  of  tiie  science  of  reasoning;  whde  those 
viho  have  bH)ked  and  relieil  r.pon  help  and  din  ction  fn>m  such  philoaophns, 
have  produced  nulhini;  of  importance.     Nn  person,  who  has  n»anU'  discoveries 
iQ^^cuDce  will,  up«m  reviewinu:  his  experience,  acknowlHge  either  Ihat  his 
mtndbaa'beenUdlou»e  habilually  the  mode   of    reasonin-   alwjiyi  to   be 
adopted  or  that  this  mode  was  »uig.slwd  to  him  in  ^ivtn  enses  by  his  previous 
studie««of  the  theorHriral  systems  of    reasoning  used    in  the  scho(ds.     Most 
per^oD^   indeed,  who  have  advanced  science,  have  been   so  inleul  upon  their 
concbiMon?;  Ihat,  they  have  not  coisidered  the  processes  of  Iheir  mmd.  ustd 
in  n^ainimr  those  conclusions  to  be  w(»rthy  of  ctmsideralion. 

~     Ibit  if  ihc  true  processes  of  rea.^onini;  were  underttoo<l,  rcasoners  woubl 
rertainlv  i»e  guided  to  advantage  by  such  knowli-.l-<.,  and  Ihry  would  use  this 
knowhd-e  al   an  instrument  to  assiiit  their  undeiMandinp:  in  solving  prob- 
lems in  parlicular  scieucrs.     To  assert  thai  there  is  a  science  of  reasoning  and 
vet  to  <av  thai  thi»  science  is  of  no  utility  in  advancing  those  sciencs,  tvhich 
ure  built"  up  by  nsi^onin-,  is  absurd.    Ail  men  admit  that  the  j^ivaler  part  ot 
our  Unowledn^e  is  j!ained  bv  rt-asonin-,  and  reasoning  certainly  «loc-s  not  pro- 
ceed by  chance- but  upon  some  .h-t.-rminalc  process;    and  unless  these  be 
1(  fritimatrlv  purbUCil  our  infecfnces  will  bo  fallacifes. 

Now  the  science  of  reasoning  ought  lo   inform  us  when  we  are  in   pur>u.t 
of  any  truth   which  can  be  -aincd  by  reasooing,  \That    method  we  mua  pur- 
Mio  in  order  to  gain  thai  truth  :    a..d    if   the  s^llo-ism   as  explained   by    ihe 
urilers  upon  ioirir-  be  (he  mtlhod  <.f  all  true  reasoning,  then   we  must  lind  a 
msior  and  min.M-  premises  which  w  ill  lead  us  to  the  trnih  in   quMition.     Uut 
a-ccudin-  to  all  the  author^  up.)n  logic,  when  we  lay  down  our  major  pi emise 
Avevirtuallv  assert    the  conclusion;  and    hence   we   must   virtually  gam  the 
knowled-eot  the  <leHired  truth   t.efoic  we  can  lay  down  the  pr.mises  which 
Miill  conduct  u.^  to  il,     We  r(  p.  at,  however,  .hat  the  popular  systems  of  logic, 
•ue  n<.l  only,  not  srientific  NNork*  in  themselves,  but  that  they  are  ol  no  use  to 
.cittuce     And  hencw  if  we  exj  tci  io  luy  sure  foundations  u|M.n  whuh  every 
science  can  be  built  in   all   il.eir  bcautiis  of  symeiry,  we  must  look  after  a 
l>etter  underslan<ling  .»f  thr  rui.<ming  processes  than  writers  upon  logic  Ime 
iH-e  1  -ible  to  exh.b  i  hliheito.     This  we  will  attempt  to  do  in  thn  book.     And 
we  are  aware  II  ailh    ta>k  is  mU  only  in  it.self  n   vnydilbcult  one,  |>   t  Jhal 
U.ep.'|tnlic'e.^  "^-     l^acon's  attempt  to  m.rodu  c  the 

inductivrsysturnVf  philosoj.hv  has  chartd  away  In  some  measure  llie  preju- 
dices of  m  inv  in  favor  of  thL-  Ari^torcde  iii  m  •l!i.>  1  ^.  Uat  15  icu;i  did  not  per- 
fect  the    mducfivf   .vsftiif,  and   al:h..n-h    he   hi.    Ufi   lerc   and  there  very 


rA' 


y^uhhk  Mntson  the  olhei*  processes  of  the  mind,  yfet  l\fe'4^^  <i<>t  *s^'stfe^a^|e 
th#lti^  itid  of  thetroe  princlpleJs  of  rtt!ocltta;ti^ii  he  iip^fekri^'^'lriffe  }iid'  no 
bWter  eonceptlon*  thftn  Ariistottle  knel  hl^.follOT^^fi,  ^dr  the  tttist '  fa^t,  * 
tfeerefote^  i-eadtrs  who  have  tomiied  any  opiiilbtt  tpon  stTjli  iji^tt^^a;  wijt, 
besides^the  difficulties  of  the  subject,  hitte  to  o^ftWne  prejudice's  in  their  ' 
study  of  this  book.  A  careful  study  we  believe,  however,  will  conquer  thoss 
prejudices. 

Before  proceeding  to  the  details  of  a  treatise  it  is  usual  with  writers  to 
give  some  definition  of  the  science  which  they  claim  to  teach  in  their  work, 
and  we  will  probably  be  expected  to  do  the  same.  Some  writers  have  defined 
Logic  to  be  the  art  of  thinking;  others  call  it  the  science  and  also  the  art  of 
reasoning;  and  still  others  consider  it  to  be  the  science  of  the  laws  of  thought 
as  thought.  For  ourselves  we  do  not  expect  that  any  definition  of  Algebra, 
which  can  t>e  framed,  will  assist  the  student  of  that  science  very  much  in  his 
studies,  tfnd  therefore,  a  definition  of  that  or  of  this  science  at  the  outset  we  ^ 
do  not  consider  of  importance.  But  besides  this  we  do  not  wish  by  a  defini- 
tion to  put  a  band  around  the  inquirers  thoughts  in  the  beginning.  If  a 
definition  convey  wrong  impressions,  it  must  fetter  the  mind  in  its  contempla- 
tions ;  and  to  lead  a  reader  who  has  not  yet  studied  the  science,  bj  a  defini- 
tion to  understand  the  whole  drift  of  \he  matter  would  require  a  full  exposi- 
tion of  the  definition,  i.  e.  a  full  treatise  upon  the  de^nition.  We  may  say, 
however,  that  the  present  .treatise  is  a  scientific  work,  and  that  the  science, 
whoso  principles  are  herein  set  forth,  difiiers  from  all  other  sciences  in  the 
respect  that  it  shows  the  only  keys  which  can  be  used  in  unlocking  the 
mynteries  of  any  science.  And  hence,  in  general  language,  this  work  may  be 
called  the  philosophy  of  science.  In  the  title  page  we  have  denominated  it 
the  Organon  of  Science — not  either  from  honor  or  derision  of  Axistottle's 
Organon ;  but  because  in  it  we  propose  to  show  the  instrument  or  instruments 
by  which  sciences  are  constructed.  Bacon  called  his  w*rk  the  **Novum 
Organ um,"  and  since  hi^time  several  works  bearing  that  name  have  appeared, 
all  of  which,  so  far  as  we  know,  follow  Aristottle  rather  than  Bacon. 

The  word  logic  has  so  many  vague  meanings  in  the  iLinds  of  men  at 
the  present  day  that  we  have  used  that  word  but  little  in  this  treatise;  although 
our  aim  and  the  aim  of  most  writers  upon  logic  are  so  far  the  same  that  they 
both  propose  to  lay  down  gome  method  by  which  we  may  be  guided  and 
kept  from  errors.  We,  however,  go  much  further  and  assert  that  our  method 
exhibits  the  mental  foundations  of  all  the  fciences  and  the  modes  of  their 
construction;  and  that  by  the  judicious  application  of  our  method,  whether 
the  thinkers  were  or  shall  be  conscious  of  it  or  not,  discoveries  in  any  science 
always  have  been  made,  and  always  must  be  made,  if  made  at  all.  Nor  do 
we  believe  that  we  are  endeavoring  to  excite  vain  hopes  when  we  say  that, 
the  thorough  understanding  of  this  treatise  by  the  scientific  men  of  the  world 


10     • 

c«n  not  fail  to  open  to  th%  world  a  more  prosperous  era  f«r  science  than  it 
has  had  hitlycrto.  And  therefore  we  have  the  boldness  to  call  upon  scientific 
men  and  upon  all  me  A,  who  wish  for  the  prosperity  and  adyancement  of  the 
human  race,  to  glTe  their  serious  ittention  to  it,  so  that  ictelli^nce  maj  work 
out  order  and 'happiness^  our  civilization.  • 


book:  I. 


CHAPTER  I. 

Highest  Generalization  anb  Fiest  Division^. 

In  erery  endearor  to  prosecute  science,  we  start  by  dividing  off  and 
classifying  those  entities,  which  are  familiar  to  us,  and  which  are  to^he  the 
subjects  of  our  consideration.  One  class  of  philosophers,  for  the  purposes 
which  they  have  in  yiew.  divide  the  objects  of  earth  into  the  animal,  vegetable 
and  mineral  kingdoms ;  and  under  each  of  these  classes  they  make  numerous 
subclassifications.  The  natural  philosopher,  techpically  so  called,  whose 
object  is  to  ascertain  the  effects  of  material  masses  upon  each  other  the  laws 
which  govern  them,  and  the  changes  which  they  undergo  without* affecting 
their  internal  constitutions,  commences  by  classifying  matter  into  solid' 
fluids  and  gasses.  The  astronomer,  the  chemist,  the  philologist  and  historian' 
have  each  of  them  their  subjects,  objects  and  classifications.  And  the 
necessity  of  a  proper  classification,  in  order  to  reduce  any  subject  to  a  science, 
will  readily  be  perceived  from  the  following  consideration:  Suppose  a  cer- 
tain  ^eld  to  contain  several  specimens  of  each  of  the  classes  of  animals  and 

t^i^T^  ^f'°''  ^"^  *°^''  '^  for  the  purpose  of  acquiring  knowledge,. if  his 
mind  should  not  generalize  and  classify,  though  he  might  multiply  observa- 
tions fer  half  a  life  time,  he  must  leave  the  field  eventually  without  havinc 
gained  any  scientific  knowledge.  In  order  to  succeed,  therefore,  the  naturalist 
commences  to  classify ;  and  his  field  of  9bservation.being.animaie  nature,  he 
seeks  for  the  highest  generalization,  which  his  mind  can  make,  and  which 
may  embrace  in  one  class,  all  the  objects  of  his  regard.  Each  subject  before 
him,  he  perceives,  has  something  in  common-  with  every  other  one  to-wit 
anmiation:  and  to  tlus  highest  generalization,  he  gives  the  name  of 'animal* 
to  distinguish  his  whole  field  of  research  from  other  things.    He  then  seeks 


X.. 
MM 


13  .   ' 

tor  other  less  extensive  generalizations,  and  soon  perceives  vertcbrata,  articn- 
lata  radiata  and  molusca.  Tlius  tlie  naturalist  proceeds,  and  by  classification 
alon.  he  is  able  to  gain  a  scientific  knowledge  of  the  relations  existing 
among  animals.  In  like  manner  a  proper  classification  of  those  things  about 
which  the  laws  of  mind  ari  concerned  in  reasoning,  is  indispensable  to  the 
clear  understanding  of  the  process  employed  in  acquiring  knowledge  by  reason 
ins  ■  without  a  classification  as  a  basis,  all  before  us  will  be  chaos. 

But  how  shall  the  metaphysician  and  logician  classify  ?    The  object,  at 
which  he  must  aim,  is  to  obtain  the  knowledge  of  the  relations,  or  rather  the 
knowledge  of  the  results  of  relation.  actuaUy  existing  between  the  mind 
iwelf  and  all  other  things,  which  can  b«  made  by  the  mind  the  subjects  of  its 
cognitions.    Now  every  subject  of  the  mind's  cognitions  must  bear  some 
relation  to  the  mind  itself  or  no  result  whatever  could  be  produced.    And  in 
order  to  contradistinguish  the  objecU  between  which  the  relations  exist,  from 
which  intellectual  results  are  .volvedi  the  mind  itself  may  be  called  the  ego 
and  all  other  things  the  h6n-eck).    The  *ord  son-ego,  however,  in  this  cas. 
is  not.a  negative  term  in  nwaaing,  but  a  positive  name  for  any  and  eveirything 
excepting  the  ego,  .r  mind  itself.    Th.  German  metachsicians  distinguishthe 
mind  iUielf  by  "Das  Ich,"  and  the  French  by  '•!>«''•":  ^^JJ'  J^m. 
Hamilton  has  brought  the  ego  and  non-ego  into  vogrfe  in  the  English  Nom- 
enclature.   Most  persons  will  know  that  eoo  is  the  Latin  personal  pronmin 
corresponding  to  ourV"onal  pronoun  I  of  the  first  person ;  ego  s  more  con- 
venient to  be  used  as  a  noun  than  our  pronoun  I,  a  single  Ictfcr  of  ^e  ^Ipbabet 
and  therefor,  it  is  used.    And  we  consider  these  contradistmgulshlng  term, 
to  be  apt  and  Oseful ;  for,  betwe«n  the  ego  and  the  non-ego.  we  »™  »»  """^  »' 
the  relations  and  results  in  question.    But  yet,  how  shall  weclassHy  the  object, 
of  our  cognitions  in  a  manner  which  will  evolveand  clearly  set  before  us  these 
reteUons lud  their  results.    We  cannot  ctearly  set  before  us  these  relations  by 
a  classification  of  the  various  objects  comprehended  in  thenon-ego,  according 
to  some-peculiarities  existing  inter  se,  for  this  does  not  in  a  sufflcienUy  appar- 
ent manner,  involve  theego:  and  unless  both  the  eg,  and  """-^^ '"^"^J*? 
there  can  be  no  relations  existing  between  them,  and  no  results  can  be  PrOdiCed 
rbeclassifiction  necessary,  as  a  basis  of  reasoning,  ">««/ '^of"'^:  """!''* 
the  highest  generalization;  for  to  plunge  -in  medias.res,'  and  class,  y  cert^a 
objects,  as  plantigrade,  and  others  as  degitjgrade,  only  points  out  the  Com- 
parative anatomy  and  r.lations  of  these  objects  inter  se;  and  to  cl»»lfy  ^he 
faculUes  of  the  mind  into  memory,  wni,imagimition,  etc.,  only  brings  ou    he 
relations  existing  between  these  faculties.    The  mind  itself,  or  ego.  is  not  n- 
volved  in  th.  classification;  and  consequently  the  results,  springmfc  from  he 
relations  of  all  other  things  to  ttie  mind  itself,  with  their.connectloDs  on  the 
one  hand  with  the  ego.  and  on  the  other  with  the  non-ego.  can^not  be  appre- 
cial«l  without  finding  a  generalization,  which  shall  comprehend  tlM;m  all. 


"ORq  inttBt,  tfcerelore,  «<«k'llie  lij^*st  jjencrahiatidn  of  bolt  tLc  ego' ahd  poij- 
ego  that  can  1m  made^mnd  ti^iafi:  this  for  our  atartihg  point,  descend/drnde 
:add  dasBify,  in  a  manner  tery  similar  to  tUat  pursued  by  the  naturalist  _- 

Now  the  highest  generalization  that  ourtnind  can  make  9f  both  the 
ego  and  non-^go  is  sxibtbkcb.    Exi^t^nce  is  'a  term  that  m^y  with  propriety 
be  applied  to-iny  and  ererything  of  >rhich  we  can  have  any  knowledge;, 
f^aefa  and  eatery  #hade  of  thought  and  feeling,  the  aCtiT*  prfnctjole  itiitlf  or^ 
(fl|^;  asalier,  tipace,  time  Itnd  the  Deity,  ibay  each  of  theih,  be  called  an  exist- 
■tnce;  tl^at  whioH  dan  be.^nd  is,  is  txk  iaxistence:  ^^  tiits  is  flie  h^hest 
-generalization  wlMch  w%  can  make  Of  things;  it  ihcludes  tlie  ego  and  ajlpf 
'the  non-^go,  the  mind  itseif  and  ererything  else,  of  whicli  we  can  hay^  cogni- 
tions.   Now  the  results  about  Which  We  are  concerned  for  logical  purposes,  are 
evolved  ft'ofn  ftie  relations  between  one  existe^icl,  our  iniihd  itself,  and  all  f  ther 
•exiifencea.    The  first  ditision,  therefore,  ai  e^fstence^  In  order  to  keep  i^^  re- 
lations of  the  fhind  to  olfhet  things  in  View,  mtist  beinto  the  ego  and  npn^go ; . 
thaKB  are  the  two  clashes  of  things  from  whos^  retatiohi  our  intellectual  results 
are  produced:    l*he  hf^hest  generalization  itself  of  all  thiuj^s  iXtoixX  wlilich  m» 
can  hare  any  knowledge,  can  not,  indeed,  be  ]ifoperly  cebsidei^  a  class  of 
THiNOs;  fur,  the  term  ExisTENCfi  dots- not  distinguish  things  inter  se,  but  it 
merely  distinguishes,  as  it  were,  things  frOm  n<i  things,  and  sets  up  a  state  of 
BEiNQ.    fittt  the  classification  of  things  into  the  ego  and  non-ego  certainly 
puts  before  Onr  mind,  and  exhibits  to  us  distiAcMy  tli^  mind  of  the  thinker  him- 
self, and  all  other  things  which  can  b^  the  subject}!  of  the  thinker V cognitions. 
And  rn  Order  to  make  this  classification  mori  clear,  we  may  consider  it  a 
little  farther.    We,  aN  of  us,  believe  there  are  such  existences  as^ees,  roc^, 
water  and  air,  in  short,  &at  there  is  such  a  thing  as  matter ;  we  baye  gained 
a  knowledge  Of  saehibin:^s  in  sot&e  idaahner ;  *and  we  believe  that  tbese 
things  are  not  Our  mihd,  but  that  thc§r  exist  otid»ide  of  it,  and  are  wha^^  f^e 
denominate*  tlie- noi-e^o.   .We  belteve,  also,  ttat  there  >re  siicb,  things  as 
notions,  thoughts,  conceptions,  feelidgs,  meiiuhs,  etc.,  and  although  these  ar^ 
ratimately  connected  wfth  the  ejg^o  *  lidd  could  not  exist  without  it,  yet,  tj|^y 
are  not  the  ihlnd  itself,  6ut  they  are  of  the  msTn-ego.    'there  is  a  wiile  differ- 
ence'^tWeen  ttie  thought^,  feeling  etc.,  produced,  and  the  active  prin^cipley 
let  itb6  What4rm«y,  which  is  ehgaged,  in  some  manner  in  their  productioj^ 
Matoyof  the  t&oii^hts  of  Shakespeare  caii  be  fodnd  inal>ook:   the  activ^ 
principle,  his  mind  itself,  can  not  be  foUbh  on  pap^rj  his  work^  are  tbe  pr<>7 
ducttons  of  hi«  niind,  not  lili  mind  itselfl    But  agaia,  ifie  believe  pujr  pwa 
min^lg'  to  exist,  and  that  oflhier  men  have  minds.    NoW  luy  mind  is  to  a^  tb^ 
egb,  but  all  other  ipinds  in  reference  to  my  mind  belong  to  the  npn-ego;  for 
every  portion  must  make*  his  DWh  n^ind  idode  the  point  from  wlxich  and  \jf^ 
whieh^ie'  mnst%iak«  all  his  beariogs^  in  gainihg^kno wledge.    But  agaip  mfe 
belicre  that  there  Is  apace,  ti lie,  eternity  and  that  there  is  a  God;  and'i^i 


14 
these  things  are  non-ego;  my  mind  ilself  only  for  me  and  year  mind  only  for 
you  are  the  ego;  all  other  things  belong  to  tCi  non-ego. 

Now  for  further  clas^fications,  we  have  to  deal  onljr  with  theoon  ego: 
for  th«  ego  being  a  single  ejcistence  is  incapable  ot  diVisjon  and  subclassifi- 
cation ;  but  the  non-ego  is  capable  of  division  i^  infinitum,  and  therefore, 
•wie  may  n  ake  numerous  subclassifications  of  it  The  non-ego,  hQwerer, 
must  always  be  subclassified  with  reference  to  the  ego  and  not  jnerely  with 
reference  to  the  constituents  of  the  noDr-ego  inter  se..  The  ego  and  non-ego 
merge  in  existence  and  this  must  be  borne  in  mind ;  jfor,  ipb^teyer  Relations, 
if  any,  may  exist  between  the  earlh  and  thennoon,  they  n^ver  could  be  any- 
thing to  us  unless  each  of  these  objects  sustain  some  relation  or  relations  to 
the  ego.  my  mind  for  me  and  your  mind  for  you.  That  which  bears  na  re- 
lation to  the  ego  can  not  be  the  subject  of  our  cognitions  and  H  must  be  to  us 
as  though  it  had  no  existence;  it  is  only  by  means  of  the  relations  of  objects 
to  &ur  minds  that  we  can  gain  any  knowledge  of  the  relations  existing  be- 
tween the  objects  themselves.  In  our  classifications,  therefore,  it  is  impor  - 
tant  to  keep  in  view  and  take  .the  ego,  my  mind  for  me  and  your  mind  for 
you,  as  the  point  from  whioh  to/un  to  every  object  of  the  non-ego. 

•     CHAPTER  II. 

« 

Tacts  and  Truths. 
Having  in  the  previous  chapter  divided  existences  into  two  clasjes  in 
such  manher  tliat  the  relations  between  them  will  always  involve  the  mind 
as  one  of  the  things  related,  we  come  "how  to  the  classification  of  the  non- 
ego  with  reference  to  the  ego.  Anfl  a.  very  obvious  diiisioi  of  the  oon-ego 
with  referenc6  tathe  ego  weuid  be  into  existences  o^  the  pas*,  of  the  present 
and  ot  the  future.  Most  of.  us,  no  doubt,  have  had  /riends  whose  phj  sical 
forms  have  piasscd  away ;  their  forms  were  existences  in  the  past,  bnt  in  the 
present  they  do  not  exist;  apd  to-morrow  is  but  a  present  themght  concern- 

ng  the  future.  But  we  must  observe  that,  these  divisions  onlj^  bring  out 
the  relations  between  points  of  time,  in  one  of  whlob  points  the  ego  is  now 
situated ;  nevertheless,  as  the  ego  and  non-ego  are  existences  bearing  towards 
each  other  th^  relations  of  time,  these  divisions,  according  to  the  po4Bt«»of 
time  occupied  by  each,  do  bring  to  view  the  relations  between  the  ego  occu- 
pying the  present  pointy  and  those  existences  of  the  non-ego  occupying 
the  same  and  ^Jifferent  points.  But  all  the  existences  comprehended  in 
the  non-ego  may  be  thrown  into  another  claisificationi  which  shall  inyolve 
the  relations  existing  between  the  ego  and  non-efo  in  other  respects  than 
thatt^f  time  and  of  that  as  well.  ^  ^  »        \ 

*  The  first  sub-classification,  therefore,  of '  the  existences  ot  the  non  -ego, 
which  we  will  make,  will  be  into  pacts  and  truths.  And  in-order  tbat  we 
may  understand  this  division,  it  is  necessary  t«  consider  the  relations  of  the 


15 
ego  merely  as  an  existence  anu)ng.  other  existences.    That  which  has  had   a 
beginning,  must  have  been  brought  icto  existence  by  some  anterior  existence 
or  existences.    We  will  not  stop  to  argue  this  point  now,  for  we  da  not  think 
it  will  be  doubUd.    And  if  our  minds  have  not  always  existed,  their  very 
beginnings  of  existence  must  be  dependencies;   and  dependent  existences 
come  and  remain  as  existences  by  the  influence  of  that  up6n  which  they 
depend.    And  when  olher  existences  like  itself  with  respect  to  dependence, 
•urround  the  ego,  the  ego  and  these  ether  existences  must  be  so  related  to 
each  other  that  they  may  act  and  re  act  Upon  each  other,  if  each  be  affected 
hj  the  other:  and  each  is  either  affected  by  the  other  directly  or  indirectly 
or  the  one  only  is  effected  by  the  other,  oi;  neither  the  one  dt)r  the  other  is 
aftecied  by  the  circumstance  of  their  both  being  existences.    Kow  between 
material  objecU,  it  is  declared  to  be  a  Hiniversal  law  of  nature,  that  action 
and  re^ctioh  are  always  equal  and' in  opposite  directions.    Whether  this  law 
be  extended  to  the  relations  between  mind  and  mind,  and  between  mind  and 
matter,  it  is  not  necessary  now  for  us  to  inquire.    But  of  one  thing  we  must 
feel  assured,  that  the  external  nop-ego,  when  its  existence  is  the  immediate 
subject  of  our  cognitions,  acts  directly  or  indirecily  on  the  ego.    For  a  tree 
either  acts  upon  and  affects  the  mind,  or  to  change  the  expression,  the  mind 
is  affected  hy  it  in  some  manner,  or  the  mind  can  have  no  cognitions  of  the 
existence  of  a  tree,  and  it  would  be  to  Uie  mind  as  though  it  were  not     The 
mind  had  a  beginning  and  therefore  it  is  a  dependent  existence;  and  an 
existence,  whose  coming  to  be  an  ezistence  is  dependent,  must  ab  initio  be 
passive:  and  its  activity  and  pasivity  both,  must  hare  been  eittter  given  to  it 
Bimultaneously,  or  the  former  must  have  been  developed  from  (he  later.    For 
the  acting  power  of  a  dependent  existence  can  not  exist  of  itself  ind^ndent 
of  other  things,  but  another  or  other  existences  are  presupposed  to  generate 
it.    And  if  the  ego  be  dependent,  iu  dependence  must  be  upon  the  external 
non-ego,  otherwise  it  would  be  independent;   and  dependence  implies  the 
reception  of  action.    The  dependent  mind,  therefore,  is  dependent  fgr  its 
existence  upon  the  action  of  that  part  of  the  non-ego,  from  which  its  exis- 
tence came,  and  for  its  knowledge  upon  the  action  ot  that  part  Of  the  external 
nen-ego,  of  whose  existence  it  gains  knowledge. 

Now  at  the  first  with  respect  to  knowled^,  other  existences  act  niion 
the  mind  without  its  inherent  energy  being  exerted.  That  we  are  bom  with- 
out any  knowledge,  will  not  be  doubted  by  anyiwell  informed  student  since 
the  days  of  Locke.  The  mind  must  exist  for  a  ceruin  period  in  its  incepiion 
without  consciousness:  for  to  be  conscious  at  all,  it  mi^t  be  conscious  of 
something:  to  be  conscious  of  noUiing  is  to  be  without  consciousness  •*  if 
consciousness  can  be  contained  m  mere  pasivity  then  a  rock  can  be  cmiieiout 
But  activity  is  necesssary  to  consciousness:  and  mental  activity  musl  be  de- 
veiopea  from  the  mind's  passivity  by  the*action  of  that  part  of  the  non-ego 


^^ 


16 

upon  which  the  mind'«  depeudtpce  in  this  respect  cougisU.  For  the  power  lo  re^ 
ceTve  an  action  mu^t  Xje  contegiporaneou*  with  the  mind'*  existence :  .but  the 
mind  must  exist  in  the  world  before  it  can  be  acted  upon  by  Any  power,  other 
than  that  Which  created  its  being  before  it  was  really  a  mind.    When,  therefore, 
the  ego  first  coines  into  the  relations  of  that  part  of  the  non-eg«,  from  which 
lU  existence  was  not  derived,  It  must  first  be  acted  «pon  aid  act  in  resi^nse 
•before  it  can  be  conscious  of  that  part  of  the  non-egoi    And  when  ^e  reflect 
that  the  external  non-ego  afects  the.  mind  only  through  the  gensei,  and  that 
in  the  foetal  state,  all  these  senses,  even  that  of  touch  in  «  great  measure  at 
least,  are  securea  against  external  impressions,  we  can  not  doubt  that  tlii 
mind  at  first  is^nconscious  of  an  external  world.    And  the  only ^ther  thing* 
of  which  it  could  be  cQnscrous,  Are  the  action  or  actions  of  the  power  which 
caused  it  to  exist,  aod  oX  yis  own  existence.    Now  the  action  of  that  existence 
or  of  those  existences  which  created  the  mind,  must  still  cohtinue  to  be 
exerted  or  the  ego  becomes  either  an  independent  existence  or  a  nt)n-cntity. 
Bat  we  have  shown  the  mind  to  be  dependent,  if  it  had  a  beginning;  and 
therefore  we  may  with  matured  faculties  appeal  to  our  consciousness  respect- 
ing the  action  of  that  creating  power,  and  all  persons  will  say  that  they  are 
entirely  uncoiiscious  of  the  action  of  that  power  which  prolongs  our  existence, 
it  is  however,  commonly  said  that  we  are  conscious  of  our  own  existence, 
i  e  \hat  the  ego  is  conscious  of  iUelf  per  se;  but  we  rtgard  this  as  an  error. 
For'unless  the  mind  act,  it  can  not  be  conscious  at  all :  and  when  it  does  act, 
it  is  conscious  of  Iti  acts,  states  and  feelings;  but  of  itself  per  se  it  U  not  con- 
scious.   Each  person  can  test  the  truth  of.  this  by  his  own  consciousness 
And  if  the  mind  at  first  be  unconscious  of  the  action  of  the  external  world 
through  the  senses,  and  also  unconsciousness  of  the  powers  which  prolong 
our  existence  and  jinconscyousness  too  of  its  own  existence  per  se  it  must  at 
first  be  without  consciousness.    The. mind,  indeed,  can  be  conscious  of  lu 
own  kcts  and  feelings;  but  independently  of  the  action  of  other  existences 

upon  it,  it  can  not  begin  to  act  Dr  to  teel. 

'   Now  we  find  that  a  material  body  made  up  of  bones, muscles,  cartilage-, 

membranes,  nerves  etc.,  t^!l  of  which  belong  to  to  the  non-ego,  coniains  the 
mind     This  body  Is  related  both  to  other  existences  without  and  to  the  mind 
within-  it  is  a  medium  betw^em  the  mind  and  existences  external  to  itself. 
And  the  first  effect  produced  upon  the  ego  by  or  through  this  body  §!▼•«  th« 
min^  merely  that  s^te  of  activity  which  we  call  intensified  P*»ivity.    The 
'  mind  does  not  yet  notice;  but  It  possesses  more  than  mere  passivity:  it  doei 
not  yet  pu^  fbrth  Its  energy  In  any  definite  direction,  but  it  possesses  energr- 
BTit  fn  a  little  time  alter  birth,  by  being  continually  acted  upon  by  \he  exUr- 
nal  world  through  the  senses,  the  mind's  intensification  is  i.creascd,  aa4  ifa 
energUstart  in  definite  directions,  and  then  it  notices.    But  it  merelynoticeik 
By  the  eye,  the  ear  and  the  other  senses,  it  notices  existences :  but  the  whbke, 


17 

the  WHEN,  the  what,  or  the  why,  it  does  not  know.  But  in  a  little  more 
time,  the  mind  begins  to  discriminate  and  then  it  begins  to  know  and  to  have 
knowledge. 

Without  the  power  to  discriminate,  we  could  know  nothing,  although 
Ve  might  notice  some  things :  and  the  possibility  of  discriminating  lies  in 
the  relations  between  the  non-efio  and  the  ego.  Now  the  only  relations, 
which  can  exist  with  referecce  to  the  ego,  between  the  existences  among 
which  the  ego  is  placed,  and  with  which  ihe  ego  itself  must  be  contemplated^ 
are  those  between  the  ego  and  external  non-ego  directly,  those  between  on© 
external  object  and  an  other  of*  the  non-ego  indirectly  through  the  ego,  those 
between  one  external  and  one  internal  object  of  the  non-ego  through  the 
ego,  and  those  between  one  internal  object  and  another  of  the  non-ego. 
From  each  of  these  relations  and  from  them  only  can  we  discriminate  and, 
gain  knowledge.  From  the  relations  existing  between  the  ego  and  the  external 
non-ego  directly,  we  have  the  action  of  the  non-ego  upon  the  ego,  and  the 
response  of  the  mind  itself  in  a  directly  opposite  direction  to  the  one  received; 
This  is  the  mere  noticing  of  an  object  by  the  mind  and  it  constitutes  a  fact. 
But  if  in  the  noticing  of  an  external  object  of  the  non-ego,  which  is  a  fact, 
the  mind  also  notices  its  own  Set,  which,  we  think,  is  the  case,  here  is  another 
thing  noticed,  a  fact  diflerent  from  the  former,  and  these  two  facts  may  be 
compared.  And  let  the  sanic  process  be  repeated  with  the  same  external 
object  of  the  non-ego,  and  we  have  a  relation  between  two  acts  of  the  mind 
itself,  between  two  internal  objects  of  the  non-ego;  and  also  a  relation  be- 
tween each  act  of  the  mind  and  the  external  object.  And  hence  among  these 
relations,  three  comparisons  may  be  made,  viz.,  between  each  act  of  the  mind 
and  the  external  object,  and  between  the  two  mental  acts  inter  se:  and  from 
either  of  these  comparisons,  the  mind  can  gain  knowledge.  From  the  com- 
parison between  the  action  of  an  external  object  of  the  non-ego  upon  the 
ego  and  the  act  of  the  mind  itself  in  return,  we  gain  the  knowledge,  that  the 
act  of  the  mind  itself  and  the  action  of  the  external  object  are  separate 
existences:  and  from  the  comparison  between  two  acts  of  the  mind  itselt,  we 
can  also  discriminate  and  gain  the  knowledge  of  separate  existences.  For 
two  acts  of  the  mind  in  the  same  direction  can  not  be  simultaneous:  and  the 
interval  of  lime,  however  small,  forms  a  relation  by  which  the  mind  can 
discriminate  and  separate  internal  existences.  Separate  existsnces  hereafter 
we  will  call  hetera.  (Greek— heteros,  a,  on-yothers).  We  use  the  neuter 
plural  of  the  Greek  adjective  as  a  noun^  meaning  other  things — separate 
existences.  And  hence  the  evolution  of  hetera  by  the  mind  is  the  inception 
of  human  knowledge.  By  the  mere  noticing  of  an  object^  the  mind  indeed 
acts,  but  can  know  nothing,  because  one  object  per  se  can  not  be  compared 
and.discriminated.  But  if  the  mind  notices  its  own  acts  in  noticing  external 
influences  and  compares  them  with  that  of  the  thing  noticed,  from  the  rela- 


18  • 

tion  existing  between  the  two,  the  mind  can  evolve  the  knowledge  of  hetera. 
And  we  must  here  remark  again,  that  the  mind  does  not  and  can  not  notice 
itself.  Its  acts,  states  and  feelings,  it  can  BoMce:  but  the  knowledge  of  its 
own  existence,  as^  potential  mind  per  se,  is  gained  only  by  comparison. 

Now  things  merely  noticed  by  the  mind  we  call  facts:  the  knowledge 
gained  by  the  comparison  of  noticed  existences,  we  call  truth:  and  this  is 
our  first  classification  of  the  existences  of  the  non-ego.  Facts  then,  are 
existences',  each  one  of  which  is  noticed  by  a  single  act  of  the  mind  and 
without  comparison :  truths  are  the  results  of  comparisons  made  by  the 
mind  between  facts  and  also  between  truths  themselves.  Now  facts  are  all 
comprehended  in  the  non-ego,  and  of  them  we  m^y  niake  two  classes :  the 
one  class  having  their  where  without  and  the  other  liaving  their  w'HEKE 
within  the  ego.  The  first  of  these  classes  we  will  call  perceptional  and 
Jhe  second  selfconscional  facts.  And  although  neither  of  these  terras  are 
in  common  use  in  our  language,  we  tliink  we  have  tlie  ri^ht  to  adapt 
terms  to  our  own  purposes.  From  the  Latin  fractio,  we  have  fraction,  from 
"Which  the  adjective  fractional  is  constructed :  and  from  perceplio,  we  have 
perception,  from  which  in  like  manner  perceptional  may  be  made  in  har- 
mony with  the  principles  of  our  language.  And  thus,  also,  we  may  deal 
with  conscio  and  prefix  sellT 

Aijd  each  of  theses  classes  of  facts  may  again  be  divided  into  five  sub- 
classes. Perceptional  facts  are  naturally  subclassified  into  the  five  classes, 
viz.:  visual  and  auricular  facts,  facts  of  touch,  of  taste  and  of  scent.  And 
hence  one  external  aggregate  existence— and  by  aggregate  existence  we 
mean  an  existence  to  which  we  can  apt^ly  our  o/gans  of  touch,  of  taste,  of 
smell,  of  sight  and  hearing— may  contain  five  perceptional  factS  or  exteinal 
noticeable  «xistences.  Such  an  existence  as  red,  or  an  existence  to  which 
we  can  apply  but  one  specific  organ  of  sense,  we  call  a  simple  existence  and 
not  an  aggregate  one.  But  two  aggregate  existences,  then,  will  contain 
ren  perceptional  facts.  And  if  each  fact  of  the  same  aggregate  existence^ 
be  compared  with  the  others,  there  will  be  ten  comparisons  of  facts  inter  sc 
of  the  same  aggregate  existence.  And  if  we  compare  each  fact  in  an  aggre- 
gate existence  with  each  fact  in  another  aggregate  existence,  we  will  have 
twenty-five  comparisons.  And  hence  two  aggregate  existences  contain  ten 
facts  and  afford  forty-five  comparisons,  from  all  of  which  truths  can  be  gained. 

CHAPTER  III. 

CONSCIOUS  TRUTHS. 

4  • 

In  the  prccecding  chapter  we  explained  what  we  mean  by  facts  and 
endeavored  to  shoir  to  what  existences  we  apply  that  term.  We  showed  that 
those  existences  which  we  call  facts,  in  and  by  Uiemselves  separately  con- 
sidered, make  no  part  of  our  knowledge;  but  that  they  are  the  foundations 


.-Trr- 


19 

and  pre-exis(en^  substrata  upon  which  all  our  knowledge  stands  and  from 
which  it  springs.  All  knowledge  fies  in  relations,  and  the  mind  evolves  it 
by  comparisons.  Were  a  person  so  brolight  into  life  that  he  could  see  the 
sun,  i.  e.,  notice  this  perceptional  fact,  but  notice  nothing  else,  i.  e.,  have  no 
self  consclonal  fact,  he  could  not  know  that  the^un  exists.  We  can  not  say 
that  the  sun  exists  wilhout  having  the  knowledge  ©f  existence.  For,  the 
phrase  *'The  sun  exists,"  or  "The  sun  is,"  is  equivalent  to  this,  viz.:  the  sun 
is  an  existence.  And  unless  we  first  have  the  knowledge  of  existence,  we  can 
not  know  the  sun  to  be  one:  not  a  single  fact  but  facts  must  come  to  the 
mind  before  knowledge  begins.  And  when  the  mind  first  notices  a  percep- 
tional fact,  there  is. also  always  lodged  in  it  aself-conscional  one;  these  facts, 
the  one  perceptional  and  the  othejr  self-conscioual  alway  enter  the  mind  in  a 
binary  manner.  For,  as  we  have  already  said,  the  ego  unconscious  of  itsqlf 
per  se,  takes  its  place  among  other  existences  to  be  acted  upon  and  to  act  in 
return.  And  these  perceptional  and  sclf-conscional  facts  keep  coming  in  a 
binary  manner  repeatedly  befor^the  mind  compares  them  at  all:  but  when  it 
does  once  make  the  comparison,  the  knowjcdge  of  separate  existence  -is 
evolved.  This  knowledge  we  call  conscious  truth,  ^nd  hence  we  say  that 
we  are  conscious  of  an  existence  though  the  knowledge  of  an  existence  be 
not  a  fact  to  us,  but  a  truth  evolved  from  the  relation  of  facts:  the  fact  of  an 
existence  per  se  is  noticed  but  not  known  by  us. 

The  relation  of  perceptional  and  self-conscional  facts  is  necessary  to 
the  beginning  of  consciousness.  For,  as  already  said,  to  be  conscious  implies 
to  be  conscious  of  something,  and  to  be  conscious  of  nothing  is  to  be  without 
consciousness;  and  the  human  mind  had  a  beginning  of  existence  and  it  is  a 
dependent  being.  And  although,  indeed,  we  can  not  tell  by  the  proofs  which 
nature  offers,  but  that  the  materia  mentis,  s(^  to  speak,  may  have  always 
existed,  and  that  at  the  first  it  may  have  been  inclosed  within  a  human  body 
and  afterwards  handed  dowji  from  generation  to  generation ;  yet  that  there? 
was  a  time  when  our  consciousness  did  not  exist,  is  clear.  For,  the  materia 
mentis,  let  it  be  what  it  maj^  could  not,  per  se,  by  its  own  inherent  power 
separated  and  independent  of  all  things  else  in  the  universe,  be  conscious  of 
anything  except  ifself  per  sc.  And  although  the  mind  be  conscious  of  its 
acts,  states  and  feelings,  yet  that  it  is  not  conscious  of  itself,  i.  e.,  not  con- 
scious of  the  fact  of  a  materia  mentis,  our  own  consciousness  teaches  us< 
And  if  the  mind  be  not  conscious  of  the  fact  of  its  existence,  or  to  use  a 
phraseology  more  tangible  to  some  minds,  if  the  mind  can  not  feel  itself  per 
Be,  i{  must  be  a  dependent  being,  and  its  dependence  must  be  a  dependence 
in  every  respect  at  least  except  existence  alone.  And  that  the  materia  mentis 
in  such  relations  as  entitle  it  to  be  called  a  human  mind  had  a  beginning  can 
not  be  denied :  and  hence  its  conciousness  in  thoso  relations  must  have  had  a 
l)eginning  also.    And  as  the  human  mind  is  inclosed  wi'hin  a  body,  were 


18 

tion  existiDg  between  the  two,  ll.e  mind  can  evolve  (he  knowledge  of  hetera 

itself.    Is  acts,  states  and  feeling.,  it  can  .o-iee:  but  the  knowledge  of  ,t^ 
own  existence  as^  potential  mind  per  se,  i,  gained  only  by  comparLn 

Now  ihmgs  merely  noticed  by  themind  we  call  facts:  the  knowled^ 
gamed  by  the  comparison  of  noticed  existence.,  we  call  trit      «mJ  n  r     • 
our  first  Cassincation  of  the  existences  of  th'e  non '  g^   fIcts  n.  n  ar" 
ex.8,enees,  each  »ne  of  which  is  noticed  by  a  single  act  of  th^m^  'and 
wthout  comparison:    truths  are  the  results  of  comparisons  n!ade  bv  Te 
«und  between  facts  and  also  between  truths  themselves     Now  Acts  Jo  all 
comprehended  in  the  non-ego.  and  of  thcm  we  „,«y  n,akV  two  ciLses     tl^ 
one  class  having  n,eirw„EHK  without  and  the  other  having  tl^irwnE«E 
w.thin  the  ego.    The  first  of  these  classes  we  will  call  pehc^io J" and 
Jhe  second  sei.fconscional  pacts.    And  although  neither  of  t™,ms  arf 
n   common   use  in  our   language,  we  think  we  have  the  ri^t    Hdaot 
terms  to  our  own  purposes.    From  the  Latin  fraclio  we  have  fr.l,  1  7  "^ 
Which  the  adjective  fraction..!  is  constructed:  and^rZ  percenUo  w .'   7'" 
perception  from  which  in  like  manner  percep.iolj  may'^beX^  i.'    T 
niony  with  the  principles  of  our  lan'-ua-e     And  tlu,«  „! 
with  conscio  and  prefi.x  sell?  ""'="''=«•    ^nd  thus,  also,  we  may  deal    • 

classes'^'^teTcemioI^rr ,""''''  "'" '''""  '"•''^'  "»"*'"  ^<=  '"^•'"^^  '"'"  "^e  sub- 
c  asses     Perceptional  tacts  are  naturally  subclassifiod  into  the  five  classes 

T.2.:  visual  and  auricular  facts,  facts  of  touch,  of  taste  and  o?  sc^t    Z.' 

hence  one   external   aggregate  existence-an  1   by  a<rS^Lc  ^l^TL. 

Tn  "orsSTnVr  '"•"^'  ^'  ''"  •^'*'^'  '•"^  i»  oTChTt"  ,?f 

no.    cab  e  'xi  te„ces"s:cVa?'  'T°  "^^  P"^^''"°"="  ^^'^  ^  -'""»> 
cciuie  existences.    Such  an  existence  as  red,  or  an  existence  to  whipi. 

ZZ  rrr  onrS  T"  "'  -"''''  ^^  •=''"  -  ^""P>-U°ncran 
.en  perce;rion°arfa:s     An    ireaclrXf Tf  t"™^'  '""'  ^•""  ^-'""1 
1.  compared  with  .he  others,  Oiere  wi.?tren'L7rL;f  Xts^  inrte 
le  exTsTenefJT    Tl""""-    ^'"'  '^  ^'  '=°'"P-'"«  "<=''  foct  in  an  aSre- 

.ets  L  a.ordT;;r  cot-pis^  ^z^2.::i:z:^t^::i 

JOH AFTER  III. 

CONSCIOUS  TRUTHS. 


and  pre-exislen*  substrata  upon  which  all  our  knowledge  stands  and  from 
which  It  springs.  AH  knowledge  fies  in  relations,  and  tie  mind  etoLs  U 
by  comparisons.  Were  a  person  so  bro>,ght  into  life  that  he  could  see  the 
sun  1.  e.,  notice  this  perceptional  fact,  but  notice  nothing  else 7"  have  Tn 
■  sell  consclonal  fact,  he  could  not  know  that  the  sun  exist.  We  cainoTs^v 
that  the  sun  exists  wi-hout  having  the  knowledge  »f  existrnce  Pnr  ^^ 
phrase  '"^o  sun  exists,"  or  "The  sun  xs."  is  equivalen  to  J v  z  Mhe  sun' 
IS  an  existence.  And  unless  we  first  have  the  knowledge  of  eX2lc.ll  ! 
not  know  ,he  sun  .o  be  one:  not  a  single  fact  but  pac™  must  "^^  ^o  t^e 

t"onal  f!  r:,      ""''i'"'-"  ^'"''-    ^"^  "'"="  *«  "'""'  first  no  cesTprcet 
tional  fact,  there  is  also  always  lodged  in  it  a  self-consc.onal  one   these  fX 

he  one  perceptional  and  the  othe,  self-conscioual  alway  enter ^heminH- 

binary  manner.    For,  as  we  have  already  said,  the  egolconscforo?  i^ 

return.    And  these  perceptional  and  self-conscional  facts  keen  rrlil  • 
bmary  manner  repeatedly  befor*the  mind  compare   them  at  all   bnwhn  > 

■v":L°rVhi?k  '"^'r^"™""'  "^*  •'""^^''^^  of  «ex .:';.; 

evolved.    This  knowledge  we  call  conscious  .ru.h.    And  hence  we  savTh»t 
we  are  conscious  of  an  existence  thouWi  the  kBowl^rt7»  „f  T      •  .^ 

acts,  states  and  feelings,  yet  that  it  is  not  conscious  of  itself  i    e    not  onn 

IndTfl  '.rr'  '"^^"'^  "^"^^^'-^  --  cons  iTusness  ;;^^^^^^^^ 
And  If  the  mind  be  not  conscious  of  the  fact  of   its  oxWi^nnr^JV 


20 

this  body  impervious  to  the  action  of  alj  external  things,  tlftmiud  must  con- 
tinue unconscious.  And  although  it  is  often  said  that  consciousness  is.  the 
very  thing  that  distinguishes  animate  life:  yet  the  lack  of  actual  conscious- 
ness does  not  establish  the  lack  of  potential  consciousness  or  the  nonentity 
of  mind.  Consciousness  is  not  the  mind  itself:  the  materia  mentis  must 
first  exist  befo/e  consciousness  can.  And  if,  as  we  have  shown,  the  mind  in 
order  to  be  conscious,  must  be  conscious  of  something,  that  something  of 
which  it  is  conscious,  must  be  brought  to  the  mind  itself  by  the  external 
non-ego:  otherwise  the  human  mind  could  rear  a  structure  of  knowled^^e 
from  out  of  itself  and  independently  of  all  things  else  in  the  universe.  Con- 
sciousness, therefore,  as  it  can  not  exist  without  a  minn  to  contain  it,  so  like- 
wise It  can  Dot  txist  in  the  human  mind  independent  of  all  things  except  the 
mind :  without  the  non-ego  the  ego  could  not  be  conscious. 

Now  there  is  in  man  a  meteria  mentis,  or  an  immaterial  substance,  or 
it  you  please  and  as  some  suppose  an  arrangement  of  physical  organs  in  some 
manner  so  that  the  arrangement  aftords  the^onditions  necessary  to  become 
conscious  when  acted  upon:  we  start  no  question  respecting:  either  of  those 
or  of  any  theories.    What  may  be  the  essence  of  mind,  we  do  not  know,  but 
whatever  it  may  be,  we  find  it,  in  a  proper  organization,  to  bo  capable  of 
knowledge;  and  our  inquiry  here  is  with  reference  to  this  knowledge.    And 
the  first  knowledge,  which  the  mind  gains,  is  cokscious  truth.    And  if 
consciousness  depend  upon  the  relations  of  facts,  i.  e.,  upon  existences  which 
are  inter  se  hetera,  it  must  spring  from  tftese  relations.    We  may  say,  that 
the  mind  has  knowledge  of  something.    This  sentence  contains  the  mention 
of  three  existences  viz. :  mind,  knowledge  and  thing."   Wo  may  say  that  the- 
mind  is  conscious  ot  somethins;  and  this  sentence  contains  mind,  coiicious- 
ness  and  thing.    And  if,  as  \^  have  shown,  the  mind  notices  its  acts,  but  not 
itself,  and  consciousness  be  dependent  for  its  existence,  then,  if  the  later  sen  - 
tence  be  true,  consciousness  must  have  been  evolved  from  the  relation  of  the 
action  ot  the  mind,  and  that  of  the  thing.    An  object  of  the  non-ego  aflects 
the  materia  mentis,  the  mind  acts;  and  from  the  relation  of  the  effect  pro- 
duced upon  the  materia  mentis,  and  the  returned  action  of  the  mind,  spring 
consciousness  or  the  knowledge  of  existence.    Consciousness  is  the  result  of 
relatiens  and  it  is  envolvcd  from  facts.    When  we  say  that  we  know  that 
stove  is  not  an  act  of  our  minds,  because  we  are  conscious  of  this,  we  state 
what  is  not  true.     We  become  conscious  of  the  existence  of  'an  act  of.  mind 
aud  of  a  stove,  and  the  judgment  then  discriminates  between  the  twg  by 
comparison.    Conciousness  is  merely  the  knowledge  of  existence;  and  the 
thing  or  existence  of  which  we  are  conscious,  we  call  a  conscious  truth. 

Now  we  have  shown  that  there  are  perceptional  and  sclf-conscional 
facts;  there  will  be  evolved  therefore,  from  the  relations  of  these  two  chisses 
conscious  truths  grounded  in  the  non-ego  and  also  conscious  truths  grounded 


21 
in  the  ego.  And^s  numerous  as  the  perceptional  and  ^elf-conscional  facts 
may  be,  so  numerous  will  be  the  conscious  truths.  For  every  relation  be- 
tween perceptional  and  self-conscional  facts  evolves  twocoifSciONAL  truths. 
The  relation  between  the  perceptional  fact  of  a  tree  and  the  self-conscional 
fact  of  the  mind's  act  in  noticing  that  tree  evolves  two  conscious  truths  the 
one  being  external  and  the  other  internal.  From  the  relations  of  self-con- 
scional facts  inter  se,  however,  or  from  the  relation  of  perceptional  facts 
inter  se,  conscious  truths  can  not  spring.  From  the  relations  of  perceptional 
and  self-conscional  facts,  spring  conscious  truths,  and  then  these  conscious 
truths  can  be  compared  promiscuously.  Conscious  truths,  therefore  like 
perceptional  and  self-consci«nal  facts,  upon  which  they  immediately  depend 
come  to  the  mind  in  a  binary  manner.  * 

Now  by  each  of  the  five  senses,  the  mind  notices  perceptional  fact^- 
when  these  facts  by  their  relation  to  self-conscional  ones,  rise  into  conscious  ' 
ness,  they  become  conscious  titiths  which  are  grounded  in  the  non-etro     So 
likewise  when  self-conscional  facts  from  their  relation  to  perceptional  one. 
rise  into  consciousness,  they  become  conscious  truths,  which  are  grounded  iu 
tlieego.    There  are.  then,  two  great  classes  of    conscious  truths  viz-  con- 
scious trutJis  grounded  in  the  non-ego,  and  conscious  truths  grounded  In  th'e 
ego.    r>ut  that  the  one  class  is  grounded  in  the  ego  aud  the  other  in  the  non- 
ego,  is  not  determined  by  consciousness,  i.  e.,  we  are  not  conscious  of  th-U 
but  this  knowledge  arises  from  an  act  of  judgment  in  comparing  two  con' 
scfous  miths,  i.  e.,  two  existences  iff  which  which  we  have  become  conscious 

^ow  It  is  said  by  some  piiilosophers,  that  the  mind  does  not  occupy 
space,!,  e.,  that  space  is  not  necessary,  not  one  of  the  conditions -of   its 
existence.     But  nothing  certainly  can  be  more  absurd:    for  that,  which  does 
not  exist  ANYwiiERE,  can  havero  existence.    Because  we  can   not  tell   the 
precise  wheue  in  which  it  does  exist,  does  not  prove  that  it  hasnotawHERF 
in  which  to  exist.    That,  which  has  an  existence  NOwnERE,Jias  no  existence 
at  all:  anf  every  where  is  a  where  infbace.   The  ego  exists  somewherf 
and  in  this  WHERE  lie  the  conscious  truths  grounded  in  the  ego-    the  non- 
«go  exists  somewhere  and  in  this  where  lie  the  conscious  truths  o-rounded  in 
the  non-ego:  the  wheres  of  tlie  ego  and  of  the  external  nou-e-o^  are  heteri 
of  si>ace.    Now  we  must  recollect  that  the  conscious  truths  gro°unded  in  the 
ego  aud  those  grounded  in  the  non^go  come  into  existence  simultaneously - 
the  only  things  th.refore,  which  the  mind  can  discriminate,  between  con- 
scious truths  grounded  in  the  ego  and  conscious  trulhs  grounded  in  the  non- 
ego,  merely  as  exisrt?nccs,  are  the  wheres  occupied  by  each,  i.  e.,  the  wheres 
can  be  discriminated  into  hetera.    We  classify,  therefore,  all  conscious  truths 
into  conscious  truths  grounded  in  the  ego,  and  conscious  truths  grounded  in 
the  non-ego:    and  that  these  two  classes  of   t.uths  respectively  are  thus 
grounded,  the  mind  determines  by  heteratino  their  wherfs.    Each  of  these 


great  classes  of  conscious  truths  may  be  again  subcljissifio^.  The  conscious 
truths  grounded  in  the  external  non-ego  are  classified  into  conscious  truths 
of  touch,  of  taste,  of  color,  of  scent  and  of  sound;  and  the  conscious  truths 
grounded  in  the  ego,  into  hearing,  seeing,  feeling,  smelling  and  tasting.  All 
these,  both  those  grounded  in  the  ion-ego,  and  those  grounded  in  the  ego, 
are  inter  se  hetera.  A  sound  is  not  the  same  thing  as  hearing,  nor  a  scent  the 
same  as  a  souid;  any  two  of  the  same  class  or  of  ditt'erent  classes,  are  hetera. 
And  hence  of  the  conscious  truths  grounded  in  the  non-ego  there  arc  five 
classes,  and  of  the  conscious  truths  grounded  in  the  ego,  there  are  five  classes; 
making  in  all  tfrn  heteiiical  subclasses  of  conscious  trutljs. 

CHAPTER  IV. 

NOMINAL  AND  PKOPOFITIONAL  TRl'TIIS. 

In  the  last  chapter  we  endeavored  to  show  what  we  mean  by  conscious 
truths.  We  do  not  mean  my  conscious  truths,  tri^tlis  which  possess  con- 
sciousness, but  exisiences  of  whose  entity  we  become  conscious,  And  we 
showed  that  we  gain  Jhe  knowledge  of  conscious  truths  by  being  able  to 
separate  the  external  and  internal  existences  of  the  non-ego  into  heter.^. 
This  is  the  first  step  in  the  acquisition  of  knowledge.  And  were  we  not 
able  to  do  this,  all  woAld  be  chaos;  But  this  once  done,  chaos  breaks  and 
order  takes  a  beginning:  and  then  we  proceed  further  and  discriminate  in- 
ternal existences  inter  se,  and  also  external  existences  inter  sc  into  hetera. 
But,  as  yet,  we  know  heterical  existenccsrwe  have  the  knowledge  of  existence 
merely  as  existence;  and  merely  as  existence,  existences  arc  all  alike.  A 
sound,  a  taste,  a  color,  etc  ,  merely  as  existences  are  l^etera  but  alike:  they 
arc,  as  existences,  heterical  similia  (Neuter  plural  of  Latin;  similis,c— things 
resembling  each  other). 

But  sound,  taste,  scent,  color  and  touch,  being  existences  grounded  in 
the  external  nc^-ego,  may  be  further  discriminated  by  the  diflerent  modes  or 
manners  by  which  they  are  rclatecfto  the  ego.  And  hearing,  seling,  smell- 
ing, tastinff  and  feeling  being  existences  grounded  in  the  ego  may  also  be 
discriminated  inter  se  by  the  modes  or  manner  by  which  they  are  related  jo 
the  external  non-ego.  The  manner  of  receiving  visual  impressions  and  see- 
ing is  diflferent  from  that  of  receiving  aricular  impressions  and  hearing. 
And  this  difference  of  mode  or  manner,  whether  there  be  any  other  difter- 
ence  or  not,  distinguishes  the  five  classes  of  conscious  existences  grounded 
the  non-ego  inter  se,  aiul  also  the  five  classes  of  conscious  existences  grounded 
in  the  ego  inter  se.  These  modes  or  manners  by  which\he  mind  is  brought 
into  relations  with  the  external  non-ego,  belong  to  our  physical  organiza- 
tions, and  inter  se  they  are  defercntia  (Neuter  plural  of  Lntm  ditfercns,  ens 
— things  differing. 

By  DIFFERENTIA  wc  do  not  mean  difference, Init  thing*; differing,  hetera 


23 
unlike.  The  diffrtcnce  between  two  feet  and  one  foot  is  one  foot:  the  differ- 
euce  in  area  between  a  parallelogram  and  triangle  of  the  same  base  and 
altitude  is  one-half  the  area  of  the  paralellogram :  but  the  difference  l>etween 
red  and  green  can  not  be  pointed  out.  The  difference  lies  in  the  causes  of 
these  effects  upon  the  mind;  but  what  those  causes  are,  we  do  not  under- 
stand sufficiently,  so  that  we  can  contemplate  them  otherwise  than  by  the 
effects  themselves,  which  we  can  only  discriminate  into  things  differing— 
differentia.  If  we  resolve  a  ray  of  light  into  its  elements  by  the  prismatic 
•spectrum,  and  then  from  diflerent  combinations  of  elements,  each  combina- 
tion having  one  element  at  least  in  it  the  same  as  in  the  others,  we  find 
different  colors  to  result,  the  difference  between  these'  combinations,  is  the 
additional  element  or  elements  in  the  one  more  than  in  another:  but  the 
differtmce  between  the  effects  per  se  of  these  combinations  upon  the  mind, 
we  can  not  point  out.  That  these  effects  per  se  are  differentia,  hetera  unlike, 
we  know;  but  that  is  all  we  know  about  them  per  se. 

Now  had  it  been  possible  for  man  to  have  become  conscious  of  only 
one  existence,  he  never  would  have  inveoted  a  name  for  that  existence.  For 
everything  which  has  a  name,  has  leceived  that  name  to  distinguish  the  re- 
sult of  a  heteralion  of  a  diflerentiation  or  of  a  comparison  of  things.  Suppose, 
for  instance,  that  every  object  of  visi6n  had  possessed  but  one  color:  no  dis- 
tinguishing name  then  for  any  color  to  distinguish  it  from  others,  could  have 
l>een  introduced  into  language.  For  flie  word  "color,"  would  have  expressed 
all  the  knowledge  that  man  could  have  hji^l  in  that  regard.  And  although 
this  existence  (color)  would  have  arisen  into. ^nsciousness:  yet  the  only 
necessity  in  a  name  for  it,  would  have  been  to  distinguish  it  from  conscious 
truths  of  the  other  senses.  And  unless  men  became  conscious  ^f  the  very 
essence  of  existence  they  could  by  making  some  possible  discrimination 
give  names  only  to  distinguish  existences  inter  se.  And  supposing  now,  all 
the  senses  excepting  sight  to  be  wanting,  and  all  objects  to  vision  to  possess 
luit  one  color,  then  there  would  be  no  oilier  existences  grounded  in  the  non- 
ego  to  discriminate  inter  se,  and  the  words  seeing  and  color  would  have 
been  sufficient  to  d^criminate  the  parts  of  man's  knowledge.  But  suppose 
now  that  along  with  the  one  color,  one  existence  of  sound  should  rise  into 
consciousness,  here  now  is  an  existence  of  a  diflerent  mode,  possessing  Ja 
different  relation  toward  the  ego  from  color.  .  There  is,  indeed,^o  assignable 
difference  within  our  knowled-e  between  a  color  and  a  sound  per  se,  they  are 
simply  differentia,  hetera  unlike;  and  their  modes  of  relation  to  the  ego  are 
differenfia:  but  the  difference  between  hearing  and  seeing  per  se  cannot  be 
pointed  out.  The  dift'erential  mode%  of  relation,  give  us  the  knowledge  of 
the  differentia,  sound  and  color.  And  now,  upon  the  above^  supposition,  wc 
know  one  sound  and  one  color,  and  know  these  two  existences  to  be  differ- 
entia: and  to  distinguish  these  two  existences  inter  se  by  words,  two  names 


24 

are  necessary.    A  nameJor  the  one  existence  alone,  will  not  answer  to  enable 
ns  to  mention  the  other.    If  we  should  caII  the  one  color,  not  color  might 
stand  for  the  sound.    IJnt  suppose  now  ascent  also  to  rise  into  conscious- 
*  ness:  wc  have  now  three  dift'erentia:  and  if  we  wish  to  speak  of   them,  we 

must  have  three  distinguishing  terms,  one  for  each:  and  so  on  through*  the 
senses. 

And  hence  we  see  that  there  will  bo  five  generic  names  in  every  lan- 
guage, which  fjas  attained  to  any  perfection,  to  distinguish  the  five  differentia 
of  conscious  truths  grounded  in  the  non-ego.  These  names  arc  signs*of  the 
results  of  the  mind's  discriminations  by  modes  of  relatioir  among  conscious 
truths  grounded  in  the  non-ego.  A  like  discrimination  is  ul  so  in  ado  with 
like  results  among  conscious  truths  grounded  in  the  ego.  But  in  giving 
these  names,  men  arc  not  naming  facts,  nor  are  they  naming  conscious  truths 
per.se;  but  they  are  giving  names  to  distinguish  conscious  truths  inter  so. 
Facts  grounded  in  tha  non-ego  pei  se,  have  no  names  to  dislinguisli  them 
inter  se:  conscious  truths  per  se  have  but  one  common  name,  to-wit,  exis- 
tence; but  conscious  truths,  which  arc  inter  se  differentia,  have  five  names 
for  those  grounded  in  the  non-eifo,  and  five  names  for  those  grounded  in  the 
ego:  each  ot  the  differentia  is  in  langu.tge  distinguislied  from  the  others  by 
a  name.  Tiiese  truths  spoken  of,  which  are  inter  se  differentia,  and  grounded 
in  the  ego  and  in  tiie  non-eso,  we  will  call  nominal  truths:,  because  they 
are  the  first  truths  distinguished  by  differential  names.  Tiie  nominaj.  truths, 
then,  are  sound,  taste,  coloi,  touch,  scent  and  tlie  hearing,  seeing,  feeling 
smelling  and  tasting:  all  t4>»se  are  inter  se  differentia.  Wc  do  not  mean) 
however,  tliat  these  trullis  were  hisloric.\lly  the  first  truths  named.  Tlie  pro- 
genitors ol^ur  race  would  be  likely  to  give  names  to  aggregate  existences 
first,  as  they  would  come  in  contact  and  feel  deeply  interested  in  them  from 
the  beginning.  Bnt  philosophically,  when  atiempting  to  reduce  our  knowl- 
edge to  scientific  order,  nominal  truths  come  up  next  after  conscious  truths 
*     and  they  are  the  first  truths  distinguished  by  differential  names. 

Now  proceeding  with  our  inquiry,  as  w;e  have  called  differential  con- 
scious truths,  nominal  truths;  so  the  truths  gained  by  diiferentiating  nominal 
truths  inter  se,  we  will  call  primary  propositlonal  truths:  because  they  are 
the  flrjt  ones  that  can  be  exhibited  in  propositions  in  which  the  words  no 
NONE  and  N^Tdo  not  occur,  and  in  which  the  subject  and  predicate  are  not 
represented  by  the  same  nrime,  as  red  is  a  coler.  And  for  the  present,  we 
will  dismiss  from  our  consideration,  those  truths  grounded  in  the  ego,  and 
consider  those  only,  which  are  grounded  in  the  non«-ego.  SuppoSe  all  the 
existences  ot  vision  presented  to  our  ^yes  for  twenty  years  of  our  life,  to 
have  had  but  one  color,  green  for  instance:  and  supposing  all  of  the  sen.scs 
to  exist  in  a  healthy  state,  at  the  end  of  that  period,  wc  would  have  the  nom- 
inal truth  of  color,  and  some  name  to  diMlnguish  it  from  the  nominal  truths 


29 

of  the  other  senses:  suppose  this  name  to  be  color.  JVnd  suppose  that  ao- 
other. existence,  RED  for  instance,  should  then  become  a  cooBcious  truth 
Now  if  we  should  compare  this  new  existence  with  all  the  others  of  which 
we  had  any  knowledge,  excepting  green-the  first  color,  we  would  perceiye 
that  it  was  not  on  the  same  scale  of  truths,  like  any  of  them  in  aay  respect 
As  a  conscious  truth  it  is  like  them  all ;  for  all  of  them  are  conscious  truths' 
But  as  a  nominal  truth,  a  further  consideration  and  discrimination,  thU  new 
existence  has  nothing  in  common  with  any  of  them.    But  if   we  compare 
THIS  R^  with  that  GREEN,  WC  pcrceivc  that  they  both  agree  in  their  modes 
of  relation  to  the  ego ;  and  it  was  because  the  modes  of  relation  to  the  ego 
-are  differentia  that  the  conscious  truths  of  sound,  taste,  scent,  etc ,  could  be 
discriminated  into  differentia— into  nominal  truths.    But  in  the  case  of  red 
and  green,  the  modes  of  relation  to  the  ego  are  not  differentia,  but  similia 
and  hence  red  and  green,  as  conscious  truths,  can  not  be  discriminated  at  all 
into  differential  nominal  truths;  but  we  must  proceed  further  and  discrimi- 
nate inter  se  nominal  truths  (to  which  both  red  and  green  belong,  and  there- 
fore the  word  qolor  is  applicable  to  both),  into  primary  propositional  truths 
Red  is  discriminated  from  the  conscious  truths  of  the  other  senses  in  the 
same  manner  that  green  is,  and  the  name  color  may  be  applied  to  both  and  it 
sufficiently  distinguishes  them  from  the  other  nominal  truths;   but  it  does 
not  distinguish  red  and  green  inter  ge.    And  to  do.this  we  must  necesswily 
discriminate  colors-    This  we  are  able  to  do.    And  the  reason  that  wc  are 
rtble  to  discriminate  colors,  lies  not  in  iheir  modes  of  relation  to  the  e-o  but     . 
in  causes,  which  are  differentia  forking  through  mod«s,  which  are  sUn'ilia- 
the  modes  of  relation  to  the  ego  are  similia,  but  the  relations  themselves  are 
differentia:   and  to  distinguish  these  relations  inter  se  two  names  must  be 
used.    Red  and  green,  therefore,  as  nominal  truths,  are  both  distinguished  in 
language  by  the  name  color;  as  primary  propositional  truths,  the  one  is  dis- 
tinguishedbythcnameREDand  the  other  by  green.    And  hence  we  can  ' 
say  that  this  color,  this  nominal  truth  distinguished  by  its  mode,  is  among 
truths  of  the  same  mode,  distinguished  by  the  name  j^ed:  this  color  is  reix 
And  if  we  add  another  color  to  our  list,  we  must  deal  wilh  it  in  like  manner 
and  similate  it  with  the  nominal  trullis  of  color,  and.  then  differentiate  thes^' 
Rimilated nominal  truths  into  primary  propositional  truths;  and  so  on  through 
the  colors.    And  if  we  now  call  color  a  genus,  asTs  generaWy  done^  by 
logicians,  we  will   then  have  species  of  color.    And  thus  we  maV  deal  with 
scents,  sounds,  tastes  and  feelings. 

And  hence  we  see  that  primary  propositional  truths  arise  by  comparing- 
and  generically  similating  and  specifically  differentiating  non^inal  trutl^ 
And  Ihese  primary  propositional  truths,  which  as  primary  propositioaal 
truths  agree  in  eveiy  respect,  will  .of  course,  be  classed  together  i  e   wiU 
havcft  common  nmic  for  each  and  every  .one  of  the  individuals  thus  alike- 


2« 

just  as  all  Domiual  truths  inter  se  similia,  will,  as  nominal  truths,  have  a 
common  name.    Take  the  primary  propositional  truth  red.  and  suppose  two   1 
heterical  REDS  to  be  before  us:  now  two  heterical  reds  as  primary  proposi-  J 
tional  truths    are  exactly  alike  in  every  respect,  starting  from  the  pacts 
which  he  at  the  foundations  of   them.    They  are  both  perceptional  facts' 
both  are  conscious  truths  grounded  in  the  non-ego,  both  are  nominal  truths* 
and  both  are  primary  propositional  truths:  but  we  can  carry  our  discrimin- 
ation no  further.    As  primary  prepositional  (ruths,  ihey  are  alike  in  everv 
respect  in  every  step  from  facts:  and  could  we  not  at  the  second  steft  exist- 
ences grounded  in  the  non-ego,  discriminate  them  into  hetera,  they  would 
be  o  us  the  same  thing.    And  in  this  manner  are  sounds,  colors.  tastJs,  scents 
•  and  touches  dirided  and  classifled.  ' 

•    The  nominal  truthjof  sound  arc  divided  inlo  musical  and  non-musical 
And  the  pnmary  pi-opositional  trull.s  of  musical  Bound  are  again  divided 
into  rythmics,  melod.cs  and  dynamics:  these  lastare  secondary  propositional 
truths.    Non-musical  sounds  too  are  freqaemly  sukclassifled   by  calling  to 
our  m.nd  and  conncc.inK  «-ith  them  some  object  which  is  supposed  to  pro- 
duce them,  or  some  stale  or  leelins  of  the  mind  itsell,  which  certain  objects 
produce;   as  vocal,  nasal,  pleasant,  dismal,  deathly  sounds,  and  soon.    But 
there  are,  no  doubt,  thousands  of  truths  ,,orceived  by  the  mind  without  names 
to  distinguish  them     For  the  colors,  which  are  differentia,  and  the  sound! 
wh^h  are  differentia  and  so  on.  are  very  numerous,  and  only  the  very  appre!  | 
ciable  and  mark«l  difterentia  receive  dis.ineuishlng  names     Now  cons^fotfs  I 
lruths,-nominaUruths.  primary  and  secondary  propositional  Iru.bs   "^°Z 
our  knowledge  of  those  simple  existences,   which  we  will   have  occastn 
hereiWter^o  call  facial  gregaria.  wcasion 

CHAPTER  V. 

OBDINAI,,  C.^RDINAI.  AND  TKMPORAI,  TKITHS.  AND  TIME  AND  SPACK      ' 

Having  in  the  last  chapter  treated  of  those  existences,  which  we  will 

^occasion  to  use  again  in  our  inquiries  under  the  nameo    fuc  .1  gT^aTla 

we  must  now  proceed  to  classify  still  other  truths,  which  enter  into  our  daM^ 

concerns  of  life,  and  from  which  we  continually  reason.    We  hav.  a  rtadv 

shown  hetera  to  lie  at  the  very  foundation  of  our  knowledgr  And  altlouS 

theuNiT  IS  the  tirst  ol  the  series  of  cardinal  lumbers  and  the  SL^  of  tf.« 

system.  Jet  duality  or  plurality  is  necessary  to  our  knowUdl  oMh.  «!? 

Without  the  knowledge  of  two  existence",  at  least,  we  coulT  not  iaveie 

knowledge  of  the  unit.    For.  the  knowledge  of  one   pring,  {roTJZll, 

relations;  and  wiUi  one  existence  per  se  there  can  be'.o  n^meTal  ^a    "n" 

Now   we  have  already  seen  that,  differentia  receive  distingui  hinr«a.^o  ' 

But  heter.,  also  receive  names  to  distinguish  .hem  inter  se.    If  we  comT.?; 

one  conscious  trutU  with  another,  apd  cannot  discriminate  them  in  o  noTn 


27 
truths,  i.  e.,  into  differentia,  the  only  way  that  is' lea  for  us  to  distinguish 
thenrai  all  bynames,  is  to  mark  them  first,  second,  third,  etc., and  this  result 
is  accomplished  by  distinguishing  existences  merely  into  hetera  and  marking 
the  individuals.  These  truths,  therefore,  we  call  ordinal  truths  They 
come  to  our  minds  in  point  of  time  at  an  early  period  of  our  knowledge-  but 
they  may  not  receive  names  to  set  them  out  clearly  for  a  long  time  after- 
wards. Ordinal  truths  are  simply  the  relations  of  separate  existences  as  ex- 
istences and  their  names  aistinguish  the  individuals  inter  se.  And  hence 
these  names  may  be  applied  to  anything,  just  as  we  may  call  anything  of 
which  we  have  knowledge,  an  exijtence.  And  in  point  of  time  the  ordinal 
truths  or  numbers,  philosophically  considered,  must  come  to  our  minds  be- 
fore the  cardinal  truths  or  numbers.  And  historically,  this  appearu  to  have 
been  the  case.  We  find  tjie  ancient  Jews,  Greeks  and  Komans,  using  for  their 
notation  the  first  ten  letters  of  the  alphabet,  which  upon  reflection  will  be 
seen  to  express  much  better  the  ordinal  than  the  cardinal  numbers  and  for 
which  purpose  they  were  most  proj^ably  used  at  the  first,  and  for  which  thev 
are  now  with  us  exclusively  used. 

And  after  the  ordinal  numbers  or  truths  are  obtained,  we  have  but  to  com 
pound  or  colligate  them  and  name  the  colligations  (for  in  nature  thev  will 
be  similia  hetera  unlike)  and  we  will  then  have  the  cardinal  ttuths  or  num 
bers,    Cardinal  ttruths,  therefore,  are  coliegations  of  hetera  with  a  defer- 
ence, inter  se  of  one,  and  they  are  distinguished  in  language  by  the  names 
one,  two,  three,  etc.    And  as  each  colligation  is  a  colligation  merely  of  hetera 
the  distinguishing  name  given  to  any  colligation  may  be  given  to  a  like' 
colligation  of   thin^  diflfering  in  nature  from  the  first,  as  two  men  two 
horses,  etc.    Tke  abstract  nature  and  applicability  of  numbers  to  any  and 
everything,  is  owing  to  t^e  circumstance,  that  they  are  names  of   hetera 
which  do  not  take  iato  considenuion,  in  any  manner,  diflTerentia  in  nature' 
but  which  merely  represent  heterical  existences.    When,  however  we  applv 
these  numerical  names  to^objects  in  the  concrete,  the  objects  must  be  lieteri 
cal  similia.    We  can  say  that  a  potato  and  a  horse  are  two  existences  but 
we  can  not  place  after  the  word  two  any  dift'ereatial  name  by  which  we  can 
express,  in  the  concrete,  the  numerical  sum  of  a  horse  and  a  potato. 

But  again :  we  have  already  seen  that  facts,  the  one  perceptional  and  the 
other  self-conscional,  enter  tl>e  mind  in  ^  binary  manner,  and  from  their  rela 
turns,  acta  of  the  mind  itself  become  conscious  truths,  known  existences  Aad 
conscious  truths  grounded  in  the  ego  may  be  compved  inter  se.  and  from 
their  relations  another  class  of  truths  may  be  evolved.  If  two  acts  of  the 
mind  m  the  sauM  mode  and  direction,  be  discriminated,  we  will  have  the 
temporal  truths  of  once,  twice,  thrice,  etc.  Whether  a  man  can  hear  see 
smell,  etc.,  all  at  the  same  time,  which  is  probable,  we  will  not  discues  '  But 
that  a  man  can  not  sec  or  hear,  h  e.,  that  the  mind  cannot  act  in  the  same 


28 
mode  and  direction  in  citlier  hearing  or  seeing  twice  at  one  and  the  same 
time  U  evident.  Place  an  object  before  you  and  look  at  it.  apd  then  %fter 
having  taken  your  eyes  away  fVom  it,  look  at  it  again,  and  you  will  not  say 
that  you  have  looked  at  it  twice  at  one  and  the  same  time.  The  comparison; 
Iheretore,  of  two  conscious  truths  inter  se  similia,  grounded  in  the  ego  ^ 
evolves  the  temporal  truths  of  once,  twice  etc. 

But  again:  if  we  resolve  existences  grounded  in  the  non-ego  mto 
hctera  we  will,  of  course,  perceive  a  plurality  of  existences.    And  if  the 
modes' of  relation  to  the  ego,  of  two  existences  so  resolved  at  the  sanae  time, 
be  the  same,  we  must  perceive  that  the  two  existences  do  not  occupy  thesame 
WHERE  for  if   they  did   we  could  not,  at  the  same  time,  resolve  them   mto 
hetera  '  Ued,  for  instance,which  occnpies  but  one  point,  can  not  at  the  same 
time  be  resolved  into  hetera,  into  separate  existences, into  two  redr.    Heter- 
ICAL  existences  grounded  in  the  non-ego,  which  are  related  to  the  cgom  like 
modes,  necessarily  occupy  heterical  wheres.    Each  of  these  wheres  may 
be  but  a  single  point,  which  can  not  b^esolved  into  hetera;  but  Uie  two 
wheres  must  be  separate,  and  if  they  be  separate,  that  which  separates  them 
we  call  sp^ce.    Space  is  a  truth  which  forms  a  class  of   truths  by  its^f 
alone     Wheres  are  necessarily  resolved  into  hetera,  when  we  resolve  exist- 
ences grounded  in  the  non-ego  into  hctera,  i.  e.,  existences  grounded  in  the 
non-ego  can  not  be  so  resolved  without  heterical  wheres.*   When  we  re- 
solve existences  on  the  other  hand,  which  are  grounded  in  the  ego  and  pro- 
duced by  the  ego's  action  in  the  same  mode  and  direction,  into  hetera,  we 
necessarily  resolve  TIMES  into  hetera.    Time  also  is  a  trulji,  which  forms  a 
class  of  Uuths  by  itself.    Mr.  Hume  derives  our  knowledge  of  space  from 
color     And  if  a  color  cover  sufficient  space  to  be  resolved  into  two  or  more 
somrwheres,  space  will  be  evolved  from  the  relaUon  of  those  wheres:  but 
if  only  a  single  point  of  color  so  minute  as  to  be  incapable  of  being  so 
resolved,  be  presented,  no  knowledge  of^pacc  can  be  gained  from  such  pomt 
per  se.   Mr.  Locke  obtains  all  our  knowledge  of  space  from  both  touch  and 
color  and  dismay  also  be  done  in  the  manner  we  have" stated.    Sir   Wm. 
Hamilton  calls  space  "A  native  idea  ot   the  mind,"  which  expression  seems 

to  have  no  meaning.  ,         ,    i         r 

We  have  now  shown  how  we  derive  and  classify  our  knowledge  ot 
colors,  tastes,  scents,  touches  and  sounds,  and  of  acts  of  the  mind  itself  into 
h«tera,  of  ordinal,  cardinal  and  temporal  numbers,  and  of  lime  and  space. 
And  it  will  be  seen  th%t  existence,  not  as  a  class  distinguished  from  other 
THINGS,  but  as  the  state  of  being  in  contradistinction  to  non-entity,  stands  at 
the  head  of  our  inquiries.  Existences  are  then  divided  into^perceptional  ai.d 
self-conscional  facts,  and  from  ihe  relations  of  thes^  we  evolved  conscious 
truths  our  first  class  of  truths.  We  then  found  some  conscious  truths  to  be 
grounded  in  tl)e  ego  and  others  in  the  non  ego,  and  in  each  of  these  classci 


I 


29 

we  founc;  no^iinal  Uuths,  so  called  because  they  are  the  first  truths  which 
receive  differentij#.  names.    From  the  relations  of  nominal  truths  ^nter  se, 
we  then  evolved  primary  propositlonal  truths,  so  called  because  they  are  the 
first  truths  which  can  be  used  in  propositions  in  which  the  words  no,  none 
and  NOT,  do  not  occur,  and  in  which  the  subject  and  predicate  terms  are  not 
the  same  name.    We  then  evolved  secondary  propositlonal  truths,  and  saw 
that  we  had  exhausted  those  simple  existences  which  Jiercafter  we  ♦will  call 
facial  gregaria.    We  then  evolved  the  ordinal,  cardinal  and  temporal  num-' 
bcrs  and  time  and  space.    And  we  must  still  proceed  further  with  our  in- 
miiries  before  we  commence  where  logicians  have  U8\ially^  commenced  in 
bating  of  the  reasoning  processes.    But  if  the  reader  will  liave  patience  to 
follow  us  in  our  preliminary  inquiries,  we  believe,  he  will  be  able  when  w^e 
come  to  treat  of  propositions  and  the  syllogism,  to  understand  the  whole 
matter,  and  to  escape  from  the  obscurities  and  perplexities,  which  in  our 

opinion,  have  hitherto  suia*ounded  those  subjects. 

• 

CHAPTER  VI. 

CLASSIFICATION  OP  AGGREGATE  EXISTENCES  AND  OTHER  TRUTHS. 

Having  already  considered  those  simple  existences  grounded  in  the 
non-ego,  whteh  we  shall  call  ^cial  gregaria,  we  come  now  to  the  contem- 
plation of  aggregate  existences.  We  may  find  a  color,  a  sound,  a.  taste,  a 
touch  and  a  scent," all  sifuated  in  one  location.  Two  existences  grounded  in 
the  non-ego  and  related  to  the  ego  by  Xhe  same  mode,  can  not  occupy  the 
same  where  at  one  and  the  same  time :  for  if  they  do,  the  existences  can  not 
be  hetera.  Thus :  two  colors  can  not  exist  in  the  same  where,  nor  two  sounds, 
nor  tastes,  etc.,  at  tho^same  time.  But  the  five  nominal  truths  grounded  in  the 
non-ego,  nevertheless,  may  all  be  found  co-existing  at  the  same  time  in  the 
same  where  and  forming  thefdcial  gregaria  of  an  aggregate  existence  (Gre- 
garius,  a,  um ;  gregaria,  neuter  plural— things  in  a  herd).  And  by  an  aggregate 
existence  we  mean  an  existence  composed  and  made  up  of  simple  existences; 
as  the  leaf  of  a  rose,  iron,  snow,  a  stone,  water,  etc.  These  aggregate  existences 
grounded  in  the  non-ego  possess  facial  gregaria,  some,  if  not  all  of  the  nominal 
truths  grounded  in  the  non-ego. 

But  aggregate  existences,  besides  the  facial  gregaria, have  also  capacial 
gregaria,  i.  e.,  capacities fo  receive  and  give  effects  among  themselves.  If  we 
move  two  heterical  and  aggregate  existences  towards  each  other,  we  find  that 
both  can  not  be  made  to  occupy  the  same  where  in  space  at  the  same  time ; 
one  of  them  must  necessarily  exclude  from  its  where,  the  other,  or  they 
both  could  not  remain  hetera.  This  capacial  gregarium  of  aggregate  exist- 
ences is  called  impenetrability,  and  is  said  to  be  one  of  the  primary  properties 
of  matter.  And  each  particle  of  matter  must  necessarily  have  a  where  in 
space  and  without  a  wh(?re  it  must  cease  to  be  an  existence.    Impenetrability, 


.  >» 


80 
therefore,  is  one  of  the  essential  capacial  gregaria  of  aggregate  existences :  If 
matter  did  not  possess  impenetrability  each  particle  migDl  annihilate  its 
neighbor  until  the  earth  became  a  non-entity.    And  another  essential  capa- 
cial gregarium  of  aggregate  existcBces  is  form  or  flgur«. 

But  after  we  have  gained  a  knowledge  of  matter,  i.  e.,  of  aggregate 
existences, ^we  readily  perceive  that  in  some  matter  the  particles  cohero 
rigidly,  while  in  others  they  move  freely  among  themselves.  This  capacial 
gregarium  of  the  one  and 'that  of  the  ether  are  inter  se  differentia:  and  if  we 
distinguish  these  gregaria  inter  se  we  will  have  the  classes,  solids  and  fluids. 
Then  again  fluidg  may  be  discriminated  by  their  facial  and  capacial  gre-^ 
garia:  one  will  not  have  a  like  color  with  another,  and  their  tastes  may  be 
differentia:  a  volume  of  one  may  be  tried  in  a  balance  with  an  equal  volume 
of  another,  and  their  specific  gravities  be  found  to  differ:  heat  may  be  applied, 
and  fluids  be  found  to  differ  in  the  degrees  of  heat  necessary,  ceteris  paribus, 
to  make  them  boil,  etc.  And  wherever  the  mind  can- discriminate  into  differ- 
entia, It  will  form  classes  of  fluids ;  and  those  which  are  not  to  us  differentia, 
may  be  called  by  one  and  the  same  name.  The  knowled^  of  all  classes  ot 
fluids  is  gained  by  differentiating  theii  gregariacither  facial  or  capacial :  capa- 
cial as  well  as  facial  gregaria  being  truths  grounded  in  the  non-ego. 

And  when  men  begin  to  examine  matt^  closely,  they  find  that  the 
particles  composing  one  bulk  may  be  analyzed,  i.  e.,  discriminated  into  differ- 
entia. And  hence  they  form  classes  of  what  they  call  elementary  substances, 
i.  e.,  aggregate  existences,  the  particle  of  which  can  be  discriminated  into 
helera,  but  not  into  difl'ere'ntia.  The  ancients  knew  but  four  elements,  viz : 
earth,  air,  fire  and  water :  man  has  since  found  a  great  many  more  elementary 
differentia.  And  every  differentiation,  that  the  mind  can  make,  throws  new 
light  upon  the  world  and  adds  new  truths  to  our  store  of  knowledge  of  the 
elements.  Now  the  number  ot  facial  gregariff^that  matter  may  possess,  so  far 
as  we  can  know,  when  expressed  In  the  classes  of  nomln^  truths,  is  five. 
Each  of  these  five  classes,  however,  are  divided  into  numerous  primary  pro- 
positional  truths,  which  have  names,  and  besides  these  there  are  various 
other  classes  of  which  we  have  knowledge  but  for  which  We  have  no  names. 
But  the  number  of  capacial  gregaria  of  matter  is  found  out  slowly,  one 
after  another:  and  where  the  number  ends  we  can  not  even  guess.  Each 
generation  to  come  may  find  out  new  capacities  of  Matter,  and  when  they  do, 
they  will  ot  course  make  new  classifications  ^cording  to  tlie  differentia  dis- 
covered. 'We  have  matter,  now,  classified  by  its  specific  gravity,  its  attraction 
of  cohesion,  its  friability,  its  ductility,  its  maleability,  its  compressibility,  its 
effects  received  and  produced  among  existences,  etc.  Any  capacial  gregaria, 
which  are  inter  se  differentia,  may  produce  classes  of  matter.  Chemestry  is 
a  suctession  of  differentiations  of  elements  and  compounds,  i.  e.,  capacial 
gregaria  discovered  by  experiment.    And  what  is  Yery  strange,  the  mineral 


^ 


i 


I 


•n 


5 


81 
enter  into  compounds  in  a  binary  manner,  as  truths  are  compounded,  so  to 
speak,  in  a  proposition  as  we  shall  see  by  and  by.  Thus:  carbon  and  oxygen 
unite  and  form  carbonic  acid:  hydrogen  and  nitr<5gcn  unite  and  form 
amonia:  and  then  the  carbonic  acid  and  &monia  unite  and  form  the  carbonate 
of  amonia.  Now  the  mental  process  of  similating  and  differentiating  hetera, 
gives  us  all  the  classes,  which  we  possess,  of  the  different  kinds  of  com- 
poficds  and  elements.  The  classification  of  matter  by  differentiating  its 
capacial  gregaria-,  so  far  as  it  has  been  accomplished,  may  be  found  in  works 
on  chemistry  and  materia  medica.  And  we  must  perceive  that  aggregate 
,  existences  when  stript  of  their  facial  and  capacial  gregaria,  are  unknown  to 
us.  The  gregaria  are  the  only  things  of  which  we  hare  any  knowledge 
through  the  senses.  That  which  lies  behind  the  gregaria  are  merely  infer- 
ences drawn  from  the  gregaria. 

Now  after  knowledge  has  increased  and  language  ]^en  invented  to  ex- 
press it,  the  science  of  grammar  takes  its  rise.  Men  begin  to  similate  and 
and  differentiate  words.  The  parts  of  speech  are  classified  by  differentiating 
Ihe  intentions  of  the  mind  in  using  different  words,  i.  e.,  by  the  functions  of 
words.  The  principles  of  the  declentions  of  nouns  and  adjectives,  and  of  the 
conjugations  and  inflections  of  verbs  arc  obtained  in  the  same  manner.  The 
knowledge  of  tense  is  gained  by  the  discrimination  of  times  into  hetera:  of 
modes  by  the  differentiation  of  manners  and  so  on. 

The  same  mental  process  also  obtains  in  Botany.  The  botanist  differ- 
entiates, cotyledons,  radicles,  plumules,  etc.,  and  as  the  plants  grow  he  finds 
buds,  which  he  in  like  manner  classifies  into  auxiliary,  accessory,  adventi- 
tious, latent  and  so  on,  he  also  differentiates  the  leaves  and  give  distinguish- 
ing names  to  each  class.  The  whole  classification  of  botany,  shows,  that  the 
human  mind  has  been  dealing  with  every  part  of  the  plant  by  similating  and 
differentiating. 

And  if  we  look  into  Zoology,  the  same  mental  process  meets  us  at  the 
threshold.  Vcrtebrated,  radiata,  articulata,  rumenants,  pachydermeta,  planti- 
grade, etc.,  are  classes  obtained  by  the  differentiation  of  truths.  And  this  can 
easily  be  shewn  to  be  the  case  with  ethnology,  entomology,  mineralogy, 
anatomy  and  all  of  the  natural  sciences.  And  hence,  each  of  those  sciences 
is  also  a  mental  philosophy  giying  us  the  classifications  of  as  many  truths 
as  the  particular  natural  science  contemplates.  Accepting  therefore  the 
classifications  ef  the  several  natural  sciences  and  making  them  our  own  we 
will  proceed  to  consider  other  truths,  wjiich  come  to  our  knowledge  from 
other  sources. 

After  having  obtained  the  knowledge  of  space  and  matter,  we  may 
easily  get  the  truth  of  extension.  Extension,  indeed,  independent  of  every- 
thing else  has  no  existence:  it  is  not  a  consious  truth.  We  speak  of  the 
extension  of  spfaceand  that  of  matter:  but  had  thercexisted  nothing  extended 


32 
extension  could  liave  made  io  part  of  our  knowledge.    And  whatever  is  ex-    ' 
tended  must  be  so  exteadcd  that  two  points  in  space,  two  somewheres,  can 
he  discriminated  by  the  mind.    And  hence  extension  when  applied  to  matter- 
means  consecutive  and  contiguous  points,  which  can  be  discriminated.    And 
in  every  other  sense,  the  word  is  misapplied ;  and  it  is  thus  when  we  use  ex- 
tension as  synonomous  with  space.    The  proper  meaning  of  the  term  exten- 
sion is  the  stretching  out  bf  something.    And  if  we  take  two  points  and  con- 
sider the  space  between  them,  and  then  remove  one  of  the  points  further  from 
ihc  other,  the  space  between  the;n  will  be  extended.    So  if  wc  consider  a 
colored  point  on  paper,  the  enlargement  of  tUat  point  will  extent  the  area  of 
the  color.    A  mere  mathematical  pomf  can  not  give  us  the  knowledge  of  ex- 
tension •  but  two  Sathematical  points  separated  from  each  other,  can  give  us 
the  knowledge  of  the  extension  of  space.    Our  knowledge  of   extension  is 
gained  by  the  discrimioation  of  heterical  points  .located  In  somMhing  in 
ppace  or  in  space  itself.    The  consecutive  points  must  all  be  in  some  cxist^- 
enceof  the  non-ego:  for  extension  is  a  truth  gained  by  the  comparison  of 
truths  grounded  in  the  non-ego.    Extension,  like  time  and  space,  forms  or 
itself  but  one  truth  and  a  class'of  tmths,  i.  e.,  there  may  be  heterical  exten- 
sions but  the  hetera  are  inter  se  similia;  there  may  be  heterical  times  and 
heterical  wheres,  but  inter  se  times  art  similia,  and  so  of  wheres,  and  there- 
fore, each  makes  but  one  class. 

But  again,  if  we  take  an  aggregate  existence,  a  piece  Of  iron  for 
instance,  and  move  it  to  another  palce,  we  will  perceive  that  it  is  not  now  in 
the  same  WHERE  in  which  it  was  before  it  was  moved,  it  has  changed  its 
place  in  space.  And  hence  the  iieteration  of  wheres  occupied  at  diflfer- 
ent  times  by  one  and  the  'same  «xistence,  gives  us  the  knowledge  of  that 
existence's  motion.  While  the  same  points  in  an  existence  remain  in  the 
same  wheres,  no  discrimination  of  any  points  wn£RES,  of  course,  can  be 
made,  and  without  the  heteration  of  one  and  the  same  poinds  wheres,  no 
motion  of  that  point  can  take  place.    This  truth  of  motion,  again,  forms  of 

itself  a  class  of  truths. 

But  again :  w«  have  in  our  minds  testimonial  truths.  And  testimonial 
truths  ai-e  those,  which  we  receive  upon  the  testimony  of  others  without 
bringing  them  up  from  facts  for  ourselves'.  And  every  witness  must  testify 
to  that  only  which  has  coaie  under  his  own  observation,  or  to  a  truth  which" 
his  own  mind  has  wrought  out:  or,  if  a  person  state  that  which  has  been 
told  to  him  by  another,  and  the  dlher  but  related  what  he  had  heard,  in 
order  that  there  may  be  any  truth  at  all  in  the  story,  there  must  have  been 
some  person,  whose  mind  broug.ht  tiie  truth  in  question  up  from  facts.  For 
some  truths,  we  are  entirely  dependent  upon  the  testipi^ony  of  others:  as  that 
Ccesar  was  assassinated,  Columbus  discovered  America,  etc.,  while  there  are 
others,  whicii  we  may  gain  for  ourselves  from  nature  and  also  receive  thera 


83 
from  testimony:  as  that  the  sun  and  moon  shine  upon  China.    And  respect- 
ing those  truths,  which  are  conreyed  to  our  minds  by  thetestimony  of  others, 
it  is  to  be  observe^J  that  there  must  always  be  some  analogy  in  the  whole  or 
in  the  parts,  between  a  truth  related  to  us  and  some  truth  of  which  we  already 
liave  the  knowledge:  otherwise  we  can  gain  no  knowledge  by  such  relation 
should  there  be  no  analogy  existing  between  the  truth,  which  a  friend  desires 
to  relate  to  us,  and  some  truth  with  ^hich  we  are  already  familiar,  no  con- 
ception of  the  truth  in  his  mind  can  be  established  by  words  in  our  own 
The  king  of  Siam  is  said  to  have  laughed  when  told  that  water,  a  fluW,  would 
congeal  and  become  ice,  a  solid :  but  if  he  had  had  already  no  knowledge  of 
a  solid  or  fluid,  he  would  liave  had  nothing  at  which  to  laugh:  for  he  could 
have  known  nothing  about  the  subject  of  the  conversation.    If  a  traveler 
should  discover  in  some  unexplored  country  an  animal  with  0et  like  those 
of  a  cow,  a.botty  like  that  ©f  a  lizzard,  and  a  head  like  that  of  a  crane  hv 
using  these  things  with  which  we  are  familiar  K)  explain  the  appearance  of 
the  various  parts  of  this  newlj^iscovered  creature,  he  could  give  us  a  con 
.    ception  of  his  animal  as  a  whole.    But  should  a  traveler  discover  an  animal 
-.4   which  in  the  whole  and  in  the  parts,  was  entirely  unlike  anything  of  which 
.    we  have  any  knowledge,.he  could  not  possibly,  by  language,  give  usany  con- 
.    ception  of  what  hejiad  seen.    And  in  order  that  we  might  gain  any  knowl- 
1   edge  of  Puch  an  animal,  we  would  have  to  see  the  animal  itself  or  have  a 

pictupe  or  sculptured  image  of  it  presented  to  us. 
^  But  again:  we  have  the  knowledge  of  existences  of  the  imagination 

^    These  existences  are  peculiar  and  require  some  consideration  here.    Centaurs' 
^    Sphihx,  Harpies,  Hydras,  etc.,  are -represented  to  us,  while  these  creatures' 

really  have  had  no  objective  existence  in  nature.    Yet  the  mind  per  se  has  no  * 
t    power  to  create  from  nothing  existences  of  any  kind ;  even  the  baseless  fabric 
of  dreams  is  not  the  creation  of  the  mind  from  nothing.    But  if  existences 
^    of  the  imagination  have  no  real  objective  existence,  and  if  the  mind  can  not 

Thfl?'°I-  n''"'  """^^'"f :  ''^'"^'  ^^  *^'^  ^^"^^  ^^  ^*  subjective  existences? 
Ihe  state  of  the  case  is  this,  a  centaur,  and  all  otMer  existences  of  the  imagi- 
nation, though  they  have  no  real  objective  existence  in  nature  as  a  combina- 
tion and  whole,  yet  all  of  them,  partially  in  the  parts  considered,  have  a  real   ' 
objective  existence.    A  centaur  is  an  existence  of  the  imagination  one  nart 
of  which  is  like  that  of  a  man,  and  the  other  like  that  of\  Z2    Both  of 
th^  parts  separately  considered,  have  a  real  objective  existence  in  nature 
The  imagination  unites  these  parts  and  from  their  combination  creates  an 
existence,  which  has  a  real  subjective  existence,  but  which  .as  a  whole  a. 
unity,  has  no  objective  existence.    But  had  the  parts,  separately  considered 
no  objectrve  existence,  their  unity  could  never  have  had  a  subjective  exist- 

fonL       n      ^°''^'°     J?'"'"'^"''  ""^  ancient  and  modern  times  have  been 
foim^  in  this  manner.    The  images  in  works  of  fiction,  theGods  of  Homer 


II 


84 

the  Metamorphoses  of  Ovid,  and  the  cbaraclcr  of   Ilamlei  and  Othelo  are 
creatures  of  imaginatioD,  which  have  been  collected  in  the  same  manner. 

CHAPTER  YII. 

CAUSE  AND  EFFECT. 

As  we  will  have  occasion  in  a  subsequent  part  of  this  volume  to  treat 
■  of  cause  and  effect,  it  seems  necessary  t^  prepare  the  way  by  examining  the 
manner  in  which  wc  come  by  the  knowledge  of  these  existences.  Now  we 
can  gain.no  knowledge  of  cause  except  through  effect.  We  may  know 
arsenic  as  a  metal ;  but  as  a  poison,  a  cause  of  death  to  animals,  we  can 
know  nothing  of  it  without  first  having  the  knowledge  of  the  eflect;  that 
thiscapacial  gregarium  is  contained  in  it,  is  found  out  through  the  effect. 
We  can  not  vi^objects,  which  are  potential  causes,  and  per  se  determine 
such  to  be  their  case,  a  priori;  it  is  some  effect  of  which  we  tlrst  gain  the 
knowledge,  that  brings  to  our  minds  the  knowledge  ol  cause.  But  the 
yery  instant  we  Took  upon  anything  as  an  c%t,  we  havo  the  knowledge  of 
cause-  for,  cause  and  effect  me  but  counterparts  of  each  other.  To  under- 
stand, therefore,  what  wcmean  by  cause,  it  Is  necessary  to  begin  TVith  the 

examination  of  effect.  . 

Now  an  effect,  in  general  language,  is  some  change^ produced.    \V  ith- 
out  change  there  can  be  no  effect.    If  wc  conceive  of  the  earth  as  having 
always  existed,  we  can  not  conceive  of  its  existence  as  an  effect.    W^e  do  not 
mean  however^  that  that  of  which  we  can  not  coneeivc,  can  have  no  existence : 
all  we  mean  is  that  we  can  have  no  knowledge  of  that  of  which  we  can  not 
conceive.    And  if'  no  changes  whatever  took  place  upon  the  earth,  or  in  the 
heavens  over  our  heads,  we  could  never  gain  the  knowledge  of  effect,  and 
consequently  we  could  know  nothing  of  cause.    If  we  cpnsider  pure  space, 
we  will  see  that  we  cai>  not  conceive  of  its  having  had  a  l)eginning,  or  of  any 
changes  whatever  having  taken  place  in  its  nature,  and  therefore,  we  can  not 
conceive  of  it,  as  an  effect.    The  knowledge  of  change  must  preceed  that  of 
effect  and  cause :  and  when  we  perceive  that  the  changa  has  been  produced 
hy  something  else  than  the  change  itself,  we  then  have  the  knowledge  of 
•effect  and  cause.    We  must  perceive,  however,  that  the  change  has  been  pro-  ^ 
duced,  or  we  do  not  come  to  look  upon  such  change  as  an  effect.    Suppose 
the  first  inhabitants  of  earth  to  have  looked  upon  the  moon  and  to  have  seen 
her  und*ergoiflg  in  appearance,  continual  changes,  (and  this  they  could  nftt 
have  avoided  if  they  looked  up)  could  they  have  evolved  the  truths  of   eftect 
and  cause  fT3m.these  phenomena  alone?    We  think  they  could  not.    If  tie 
•  first  changes  with  which  men  became  acquainted  were  those  of  the  phases  of 
the  moon.*and  their  minds  were  not  yet  familiar  with  the  exertion  of  any 
power  in  nature  to  produce  change,  providing  they  really  believed  the  olOt 
and  full  moon  to  be  in  rcalitj-  changes  in  the  same  moon,  indicat|^  by 


35 
phenomenal    differentia,  the    comparison  of   these  differentia  would  only 
evolve  the  knowledge  of  change.    But  that  this  change  was  the  effect  of 
some  cause,  could  not  be  evolved  from  such  coipparison. 

Now  the  simplest  change  with  which  we  are  acquainted,  and  which 
wc  can  perceive  to  be  produced,  to  be  an  eflect,  is  the  change  ©f  aggregate 
existences  in  space,  i.  e.,  a  change  of  their  wheres.  Suppose  a  man  should 
see  one  ivory  ball  strike  against  another  and  send  that  other  some  distance 
through  space ;  in  such  case  he  would  see  a  change  produced,  an  effect.  He 
would  perceive  heterical  wheres  occupied  at  different  times  by  the  one  and 
same  ball  which  was. struck,  and  also  heterical  wheres  occupied  successively 
by  the  striking  ball :  he  would  also  perceive  that  some  ©f  the  heterical 
wheres  of  the  one  ball  and  some  of  tho^e  of  the  other,  became,  at  dj^erent 
time?,  homon  (Greek— neuter  singular;  from  homos,  a,  on— tj^e  same).  If  we 
contemplate  the  two  balls,  we  perceive  that  they  are  hetera  and  that  their 
where/4  are  hetera;  and  when  the  striking  ball  moves  towards  the  other  its 
course  is  made  up  of  wheres  which  are  inter  se  hetera  until  it  strikes,  when 
the  ball  struck  makes  heterical  wheres.  But  so  soon  as  the  first  ball  strikes 
the  second  one,  some  of  the  first  one's  wheres  and  some  of  the  second  one's 
wheres  become  homon,  and  from  the  impenetrability  of  matter,  this  could 
«ot  b«  the  case  without  the  second  one  having  vacated  those  wheres.  In  this 
case  the  change  in  space  of  the  second  ball  is  seen  to  be  an  effect,  and  the 
cause  is  easily  perceived.  The  first  ball  commenced  to  move  towards  the 
second  one  until  it  touched  it,  and  had  it  proceeded  no  further,  no  effect 
would  have  been  produced  upon  the  second  one:  but  if  it  go  on  further 
some  of  its  wheres  and  some  of  those  of  the  second  must  become  homon  i. 
c.,  the  wheres  of  the  second  hall  at  one  time  and  the  wheres  of  the  first  ball 
at  another  time,  are  in  space,  homon.  Now  one  instance  of  change  involv- 
ing such  reikions,  if  contemplated,  would  give  us  the  knowledge  o(  effect  * 
and  cause. 

But  again,  if  we  ti«  one  end  of  a  string  to  a  permanent  object  and 
attach  the  other  end  to  the  one  end  of  a  lever,  every  point  in  tliat  string  will 
occupy  a  where,  and  the  wheres  of  all  the  points  inter  se  be  hetera.  The 
'end  of  the  lever  to  which  the  string  is  attached  will  also  Save  a  where,  which 
in  reference  to  any  point  in  the  string,  will  be  heteron.  If  now  the  stiiag 
contract,  some  of  the  points  in  the  string  will  take  the  wheres >of  other  po'ints 
and  some  of  the  wheres  of  the  end  of  the  lever,  and  some  of  the  wheres  of 
points  in  the  string,  which  were  at  first  hetera,  now  become  homon.  And 
hence  we  see  that  in  all  those  changes  of  aggregate  existences  in  space,  which 
we  regard  as  effects  and  whose  causes  we  understand,  we  find  heterical  ex- 
istences with  heterical  wheres,  and  some  of  the  wheres  of  one  and  of  another 
becoming  hgmon.  Change  of  objects  in  space  is  also  produced  by  what  is 
called  attraction  and  repulsion,  but  what  are  the  causes  and  modus  operandi 


iU- 


ajni^!*! 


36 

in  these  changes,  pliilesopbers  have  not  yet  sufficiently  explained  to  us.«  The 
convertiou  of  hetera  into  homon  among  wheres,  is  the  modus  operandi  in 
those  changes  of  objects  in  space,  which  we  fully  understand.  Take  a  piece 
of  iron  and  keep  it  all  the  time  for  a  certain  period  under  your  eye,  and 
during  this  period  move  it  with  your  hand  from  one  place  to  another!  In 
this  case  we  perceive  that  the  existence  moved  (the  iron)  remains  one  and  the 
same ;  but  its  wheres  successively  and  the  times  of  occupying  them  can  be 
discriminated,  and  so  also  respecting  your  hand.  But  some  of  the  wheres 
of  the  iron  and  some  of  the  hand's  wheres  can  not  be  discriminatecl,  they  are 
komon,  though  the  times  of  occupying  them  by  each  successively  are  never 
liomon  always  but  hetera. 

:^ut  again,  we  sometimes  see  one  existence  acting  upon  another,  and  a 
constitutional  change  following  such  action.  Take  a  hammer  and  with  it 
strike  a  grain  of  corn  placed  upon  a  rock,  and  we  will  see  that  a  constitu- 
tional change  takes  place  in  the  corn.  This  change  too,  we  could  scarcely 
avoid  regarding  as  an  effect  the  first  time  that  we  should  witness  the  occur- 
rence. And  in  this  case,  it  will  be  perceived  that  two  heterical  existences 
come  in  contact  and  that  some  of  the  wheres  of  the  one  and  some  of  the 
ether  become  homon :  and  further  that  some  of  the  heterical  wheres  of  the^ 
particles  in  the  grain  of  corn  become  homon,  and  hence  the  constitutional 
change.  The  grain  of  corn  possessed  rigidity  but  this  gregarium-  was  de- 
stroyed by  reducing  heterical  wheres  of  heterical  particles  to  homon.  On 
the  contrary  ignite  gunpowder  and  heterical  particles  immediately  take 
heterical  wheres.  * 

Again,  if  we  take  a  piece  of  ice  in  our  hand  and  it  melt  and  become 
water,  here  ft  a  constitutional  change;    ice,  an  aggregate  existence,  has 
changea  some  of  its  fi:regaria  and  become  water:  and  in  chalking  these 
gregaria,  heterical  wheres  ot  particles  became  homon.    And  in  this  case  we 
must  perceive  that  the  where  of  the  two  aggregate  existences,  ice  and  water 
remams  the  same  for  bpth;  but  the  existences  possess  gregaria  inter  sedifi-er- 
entia,  and  the  times  of  occupying  the  same  where  are  hetera.    And  hence 
when  there  is  during  a  certain  period  of  time  but  one  where  for  two  differ-  ' 
ential  existences,  the  one  must  have  occupied  that  where  for  a  part  of  that 
period  and  then^become  the  other  existence.    And  when  we  conceive  such  to 
have  been  the  case,  we  can  not  help  conceiving  of  a  constitutional  change 
having  taken  place.    Now  in  change  times  can  always  be  heterated  and  when 
we  can  go  a  step  further  and  heterate  wheres,  the  change  is  that  of  place. 
But  when  we  can  go  still  further  and  perceive  that  an  aggregate  existence 
has  lost  some  of  its  gregaria  and  taken  others,  which  with  reference  to  the 
first  are  differentia,  the  change  is  constitutional.    A  piece  of  iron  ahen  heated 
possesses  different  gregaria  from  those  which  it  has  when  cold :  this  is  owing 


37 

to  a  constitutional  change.    It,  however,  cools  again  and  assumes  its  former 
gregaria.  • 

But  again,  if  we  take  grains  of  white  sand  and  consider  them  all  to- 
gether in  a  pile,  we  shall  have  a  homogenious  aggregate  existence  i  e  an 
existence  in  which  all  the  particles  are  inter  se  similia:  and  consequemiy 
the  wheres  of  all  the  particles  can  be  heterated  but  the  particles  themselves 
can  not  be  diftbrentiated,  if  now  we  mix  red  sand  with  the  pile,  we  then  find 
in  it  particles  which  are  not  only  hetera  but  also  difterentia.  -lie  pile  now 
therefore,  compared  with  what  It  was  shows  change.  Thia  change,  however' 
is  owing  entirely  to  the  change  in  space  oP  the  particles  of  red  and  white 
sand.  *      •  •^ 

But  again,  suppose  we  take  an  aggregate  existence  in  which  all  of  the 
particles  arc  similia,  so  far  as  we  can  perceive,  but  by  subjecting  it  to  a  certain 
process  we  find  that  particles  which  we  regarded  as  similia Miave  become 
plainly  differentia,  which  is  always  the  case  in  the  analysis  of  compounds 
here  is  to  us  a  change  of  a  different  kind  from  any  oF  the  former.  -      ' 

And  again,  suppose  we  take  two  aggregate  existences,  in  each  of  which 
the  particles  inter  se  are  similia,  but  the  particles  of  the  one  and  those  of  the 
other  are  inter  se  differentia,  and  we  put  ^lese  two  aggregate  existences  to- 
gether and  find  that  all  the  particles  of  each  existence  now,  if  compared  with 
what  they  were  then,  arc  then  and  now  inter  se  differentia,  but  among  them- 
selves they  have  all  became  now  similia:  here  again  is  a  change  different  in 
kind  from  any  of  the  former.  This  change  always  takes  place  when  differ- 
ent elements  unite  aud  forn^  compound. 

The    following:,  therefore,  appear  to  be  the  principal  changes  with 
which  we  are  familiar,  viz:  the  starting  an  aggregate  existence  in  an  homoni- 
cal  WHERE  into  heterical  wheres,  which  is  a  change  of  place ;  the  chancre 
.  of  heterical  wheres  of  particles  into  homonical  wheres,  and  vice  versa  which 
IS  a  constitutional  change  of  the  adhesion  of  particles  inter  se,  as  in'crush- 
ing  and  expansion;  the  convertion. of  similia  into  differentia,  which  is  the 
analysis  of  a  compound;  and  the  conversion  of  differentia  into  similia  which 
is  the  synthesis  of  elements,  having  chemical  affinity  fer  each  other  '  Every 
change  which  takes  place  among  existences  of  the  non-ego  involves  theprio- 
cip?es  of  one  or  another  ot  the  above  examples,  excepting  changes  in  degree 
And  we  can  readily  see  that  one  homonical  existence  perse  can  not  change' 
but  that  the  change  of  any  one  existence  is  owing  in  part  to  some  other  exist- 
ence.   Every  change  is  dependent.    And  as  change  springs  from  the  relations 
or  existences,  within  those  relations  must  also  be  the  cause  or  power  to  pro- 
duce change.    Sodium  persse  does  not  posses  the  cause  of 'soda;   nor  does 
oxygen  contain  it  within  itself;  but  from  the  relations  of  sodium  and  oxy-en 
spring  the  protoxide  of  sodnim  or  soda.    And  we  see  that  the  knowledge^ of 
Change  comes  into  our  minds  by  comparison:  and  so  dso  does-our  knowl- 


•  % 


88    _ 

edge  of  effect  and  cause.  And  without  the  involution  of  homon  and  hel#ra, 
or  similia  and  differentia,  or  coramensura  and  iucomensiita,  we  can  not  evolve 
the  Knowledge  of  cause  and  effect. 

There  is  a  change  in  the  appearance  of  the  moon ;  there  is  also  a 
change  in  the  state  of  the  atmosphere,  by  the  comparison  of  these  changed, 
we  have  hetera  aud  differentia,  but  neither  homon  or  similia.  And  from  tliese 
things  per  se,  i.  c.,  from  helera  and  differentia,  or  from  homon  and  similia,  or 
from  hetera  ot  homon  aud  commensura,  we  cannot  evolve  the  knowledge  of 
cause  and  effect.  If  a  rock  fall  from  the  cliff  of  a  mountain  into  the  valle)% 
and  about  the  same  time  the  ice  bl^ak  loose  from  the  shores  and  float  down  a 
river,  here  also  are  changes,  iSlit  they  do  not'come  together  anywhere,  so  as 
to  bring  hetera  into  homon,  or  vice  versa ;  similia  into  differentia,  or  vice  versa ; 
commensura  into  incommensura,  or  vice  versa;  so  that  we  can  evolve  from 
their  comparison  an  effect  or  cause.  Hetera  must  meet  somewhere  in  homen 
or  vice  versa;  or  similia  in  differentia,  or  vice  yersa;  or  commensura  in  in- 
commensura,  or  vice  versa;  in  order  to  bring  to  our  minds  effects  and 
causes. 

Now  of  causes  there  are  three  classes  viz:  expended, acting  and  poten- 
tial. Causa  slriarum  of  the  rocks  is  an  example  of  an  expended  cause.  Tlie 
floating  icebergs,  as  believed,  striated  in  their  course  the  rocks.  Biit 
they  have  vanished  and  ceased  to  be  causes.  The  flawing  of  the  water  in  the 
liver  Is  an  effect  of  an  acting  cause,  and  gunpowder  \inexplodcd  is  an  exam- 
ple of  a  potential  cause.  '  •  *        . 

CHAPTER  VIII.    ^. 

NAM«S. 

We  come  now  to  the  consideration  of  names.  When  we  reason  and 
use  words,  we  must  necessarily  sec  to  it,  that  our  words  have  some  definite 
meaning,  otherwise  we  will  but  veer  about  over  subjects  at  random  wilh«ut 
making  comparisons  in  such  a  manner  as  will  evolve  truths.  In  the  most 
common  affairs  of  life  we  reason  either  well  or  or  ill,  and  we  lead  others  into 
our  trains  of  thought  and  reasoning  by  the  use  of  words.  So  much  have 
words  to  do  with  reasoning,  that  Archbishop  Whatcly  concluded  logic,  or  the 
science  of  reasoning,  to  be  entirely  conversant  about  language:  a  mistake 
similar  to  that  of  supposing  the  symbols  of  Algebra  to  be  the  only  things 
about  which  that  science  treats.  But  the  relations  of  existences  inter  j?e  arc 
subject-matter  of  the  science. of  reasoning  and  of  every  other  science.  And 
as  words  are  used  to  designate  the  results  of  these  relations,  the  words  them- 
selves must  subjectively  bear  some  relations  to  each  otJier  and  to  the  exist- 
ences which  they  are  used  to  designate:  and  so  far  as  they  are  brought  by 
the  mind  to  jjjay  a  part  in  the  relations  of  the  ego  to  the  non-ego  in  rcason- 


39 
ing,  they  are  the  subjects  of  the  science  of  reasoning.    And  after  what  has 
already  been  said  in  the  previous  chapters,  we  do  not  \hing  it  will  be  very 
difficult  to  undeastand  the  functions  of  words  in  the  processes  of  reasonino-. 

We  have  already  seen,  that  hetera  lie  at  the  very  foundations  of  »oiir 
knowletlge.  That  which  'is  so  related  to  the  ego,  that  it  may  be  an  object 
between  which  and  the  ego,  some  truth  depending  upon  such  relation  may 
come  to  our  knowledge,  we  tall  an  existence.  And  words  when  spoken  are 
to  the  car  signs  ^  cos:nitions  of  the  per;3on  speaking  them;  when  written  on 
paper  they  arc  signs  for  the  eyt.  And  when  existences  come  to  our  knowl- 
edge to  be  existences  by  the  power  of  the  miad  to  evolve  the  relations  among 
whichit  is  placed  into  hetera,  these  heterical  existences  are  known  only  as 
lietera,  and  no  one  of  them  is  distinguished  from  another  except  as  separate 
existences.  And  when  wo  consider  one  of  these  heterical  existences  inde- 
pendently of  its  relations  to  others,  and  we  wish  to  set  out  a  word  as  the  sign 
of  our  cognition,  we  use  a  name  to  call  to  the  mind  of  the  hearer  or  of  hhn 
who  sees  the  word  written,  one  of/ hetera,  without  distinguishing  in  any 
manner  this  one  from  others. 

And  hence  words,  for  logical  purposes,  mav  be  divided  into  two 
classes,  viz:  names  which  are  used  by  us  to  distinguish  existences  inter  se 
and  names  used  to  call  to  the  mind  existences  without  distinguishing  theni 
inter  se.  To  the  later  class  belong  such  words  as  existence,  being,  thing, 
entity^phenomenou,  etc.  These  non-distinguishing  names  are  few  in*number 
in  all  languages.  And  taking  up  the  second  class,  i.  e.,  names  used  by^s  as 
signs  to  distinguish  existences  inter  se,  we  will  notice  those  few  in  number 
which  distinguish  hetera  inter  se.  Names  to  distinguish  hetera ^inter  se  are 
such  words  as  the  following:  this  and  that,  these  and  those,  once,  twice,  first 
second,  Cgo  and  non-ego,  etc.  '         * 

But  every  conscious  existence  lias  a  where,  wbich  it  occupies,  and  the 
relations  of  wheres  occupied  by  conscious  existences  are  expressed  byprepo- 
.^itions.  The  where,  however,  and  the  conscious  truth  which  occupies  it,  are 
differentia.  And  we  will,  perhaps,  be  bettcV  understood  if  we  sub-divide 
that  class  of  names,  which  distinguish  existences  inter  se,*into  six  classes 
viz:  names  of  homon,  of  hetera,  of  similia,  of  differentia,  of  commensura 
and  of  mcommensura;  and  keeping  this  sub-classification  in  view,  we  will 
treat  of  them  somewhat  promicuousi3\ 

Now  it  must  be  evident  that  sometimes  a  simple  word  is  used  as  a 
name,  as  iron,  glas?,  ice,  etc.,  and  sometimes  names  are  Compound  words,*as 
hydrophobip,  etc.  All  those  words,  which  by  grammarians  are  distinguished 
as  nouns,  arc  names.  Some  of  tUcse  are  names  of  simple  exislendfes  as  red, 
tnste  sound,  etc.,  and  some  are  names  of  aggregate  existences  as  iron,  wood* 
CDal,  ship,  etc.  And  all  those  words  too,  which  are  grammatically  adjectives' 
arc  logically  but  names  ©f  the  gregaria  of  aggregate  existences.    In  the  ex- 


40 

pression,  "A  red  house,"  the  word  red  sLowa  lliat  this  facial  gregarium   is 
one  of  the  gregaria  of  the  house,  and  of  this  facial  giegariumrit  is  the 
name.    And  all  adjectives  of  the  positive  degree  when  joined  to  ac^gregate 
existences,  name  some  one  of  the  gregaria,  facial  or  capacial,  which  aion*^ 
with  others  constitute  the  peculiar  aggregation  named  by  the  noun  to  wliich 
the  adjective  belongs.  'In  the  expression,  "A  good  man,"  the  noun  man  is 
the  name  of  an  aggregate  existence,  and  the  woid  'good,»  which  i?  joined 
with  it,  is  the  name  of  one  ot   the  capacial  gregaria  suppo^d  to  be  in  the 
aggregation.    "A  fusible  metal,"  is  an  expression  of  thejsame  kind     And  it 
is  to  be  remarked  that  those  adjectives  which  are  the  names  of   facial  gre 
garia  may  stand  alone  as  the  n^mes  of  eillier  the  subject  or  predicate  of  a 
proposition:  while  names  of  capacial  gregaria  require,  generally,  in  our 
language,  the  names  of  existences  in  which  the  gregaria  named   by  them 
severally,  are  aggregated,  to  go  along  with  them  when  ihey  are  made  the 
subject  of  a  proposition.    We  can  say  that  white  or  red  is  a  color;   but  wo 
can  not  say  that  a  round  is  on  the  table;  and  we  should  rather  say  a  round 
tiling  IS  on  the  table.    And  when  wc  wish  to  use  such  words,  which  are  the 
names  of  capacial  gregaria,  as  names  by  themselves  in  the  subject  of  propo- 
sitions, we  usually  change  the  lorm  of  the  word:  thus  round  is  changed  into 
roundness,  rectangular  ipto  rectangularity,  heavy  into  heaviness  or  weight. 

The  article  a  or  an  is  continually  used  in  logical  propositions  and  it 
alwa3>ha8  a  significance.  This  article  is  tlie  name  of  an  heterical  relation  • 
itisderirecl  from  ane;  German  ein,  and  means  oke.  And  therefore  the 
expression,  "A  red  house,"  contains  three  names  viz :  house,  the  name  of  an 
aggregate  existence;  red,  the  name  of  one  of  its  gregaria,  and  a  (bne)  the 
name  of  the  numerical  relation  ot  the  house.  The  article  tjie,  is  tl.S  name 
of  an  homonical  relation,  and  it  is  used  to  distinguish  homon  from  hetera- 
as,  This  IS  the  horse  which  we  saw  yesterday,"  "Thou  art  the  man  "  etc 
Sometimes  the  adjective  same  and  also  the  word  self  are  used  alone  with  the" 
noun  to  which  the  article  refers":  as,  "The  same  horse,"  "The  gate  itself." 
The  articles,  however,  can  not  be  used  alone,  either  as  the  subject  or  predi- 
cate of  a  proposition  which  is  concerned  about  anything  else  than  names. 
They  however  frequently  appear  in  propositions  along  with  other  names, 
and  their  functions,  therefore,  ought  to  be  understood 

Prepositions  are  the  names  of  relations  among  existences  and  amon" 
the  wheres  of  existences  in  space:  as,  "The  log  nnder  tlie  brid-'e  "  "In  the 
house.  "Over  the  river,"  "Beyond  the  treo..-  etc.^  Adverbs  are  tfte'  names  ^f 
relations  <rf  time  and  space  and  modes  of  actinfi:  as  here,  there,  then,  now. 
bravely,  dilligently,  etc.    We  do  not  propose  to  treat  of  words  any  iWlh.; 

^kl'™oLTT7  •°  "r  '""'«'«'«°""'«  of  --easonins.  and  we  have  perhaps, 
said  enough  about  simple  n^ies  for -the  present. 


Bat  frequently  several  words  taken  together  make  but  one  distineuish- 
ingname:  a.  "A  red  color"  u  the  name  of  a  single  and  simpW  existent. 
Again,  "Charles  Carrol  of  Carrollon"  is  but  one^name  Ind  "The  S 
who  ground  the  grist  yesterday  and  who  died  to-day"  is  but  one  name,  aBd 
after  it  we  may  add.  "was  a  man  of  benevolence."  another  name  "In  the 
house"  and  "By  the  sea-sid."  are  distinguishing  names  of  heterTcal  whe^^ 
Such  names  are  c^led  by  logicUns  many  wobded  names 

But  again,  a  collective  noun  or  name  stands  as  a  sign  to  dlstinsuish  an 
aggregation  of  ^aggregation,:  as.  the  assembly,  a  multitude,  a  Shot 

ZuZTT  t"**  f  <="  «"<="  '">n'««ar«  «««<!.  it  is  usual  aLd  frequemly 
beuer  for  the  sake  of  perspicuity,  to  connect  the  name  of  an  aggregate  ex 

UoT'wTthtel',';  T"  °'  ""  '""""  "'""^  ■"'"«  "•»  "*«  collecffve^a^^t 
tion.  with  the  collective  noun :  as  the  assembly  of , the  people,  a  multilude  of 
women,  a  regiment  of  geese,  a  society  of  prairie  dogs,  etc  """""-"e  ot 

Again:  *«?.""'''  "^  common  name  is  one  used'io  the  first  instance  to 
distinguish  an  individual  existence,  either  simple  t  aggregate  which  h^ 
been- differentiated  or  inc.mmensurated  from  others:  but  fach  of  tTSx^r 

common     A  common  name  is  the  name  of  slmilia  or  of  commenfura     Ex- 

slences  inter  se  s  milia  never  receive  a  name  other  thap  a  common  one  for 

each  individual,  for  .he  simple  reason  thkt.  after  we  have  distinguished  Lem 

into  he  era  there  i.  nothing  by  which  we  can  distinguish  theXther     W^ 

iZhetrl     a' h'.""" '.'•"?••'""  ^"'"'  '■""'-e  distinguishes  [h  m  me  J; 
mo  hetera     And  in  order  that  any  existence  may  be  given  a  iame  to  d  ! 

nni  d?/""".r"'%".  °''*'"'*'' '"""  •^'«"'=»"^-  "  «»«»  ">«  otherTm^st  ^ 
inter  se  differentia.    If  we  take  ten  grains  of  corn  inter  se  similia  and  -call 

to  Lth?  '  T"""  ^"'' '"'°"'"  Gamm^randso  on,  our  naming  hasUonn,^ 
to  nothing;  for  so  soon  as  our  eyes  are  turned  away  from  them  andreyha^ 
Changed  places,  w.  can  not  afterwards  tell,  which  one  is  Alpha  or  BeTa  r 

fhin^T  r'"""""'-  '•""^°'«'  *•''«''  "='«'  "•'  be  discriminaUd  by  us  fu^^r" 
ban  into  he.era  must  from  a  mental  necessity,  when  not  numerLlly  con! 
sidered.  receive  from  us  a  com«oa  name.  But  it  may  be  said  that  hobse  is 
a  common  name,  yet  horses  can  be  discriminated.  This  is  true  ^ftten 
they  also  receive  distinguishing  names;  aot  indeed,  to  dis-tlnguish  the  i^dt 

A    !.      .'  distinguish  them  inter  se;  as  black  horse,  white  horse^ 

Arabian  hor...  the  horse  With  short  ears,  the  near  horse,  the  ofrZ^2 
la  ike  manner  color  is  a  common  name,  yet  colors  inter  se  can  be  discrim- 
.nau.1  mto  differentia,  which  receive  distinguishingnames,  and  wWchnamt 


(  ■• 


42 

Now  if  a  man  should  place  before  himself  a  horse,  atr^c  and  a  stona,  by 
examiniDg  them,  he  would  perceive,  that  the  one  possessed  the  capacial  grega- 
rium  of  animation;  the  other  the  capacial  grxjgaria  of  vegetation,  and  the 
last,  capacial  gregaria  of  a  different  kind  from  either  of  fhe  former.  These 
three  objects,  therefore,  would  be  inter  se  differentia:  they  are  the  three 
aggregate  nominal  truths,  and  we  may  distinguish  them  inter  se  by  the 
names  animal,  vegetable  and  mineral.  And  alterwards  every  object  possess- 
ing the  capacial-  gregarium  of  animation  and  the  horse,  as  aggrecrate  nomi- 
nal truths,  would  be  similia,  and  therefore  it  ftiust  be  called  by  the  name 
animal.  Animals,  however,  may  be  differentiated  into  aggregate  primary 
propositional  truths,  and  so  on  in  a  like  manner,  which,  we  saw  was  persucd 
with  those  simple  existences,  which  we  call  facial  gregaria  grounded  in  the 
non-ego.  'And  it  must  appeaj;,  that^f  every  aggiegate  existence,  with  -which 
■we  are  acquainted,  possessed  the  like  number  of  facial  and  capacial  gregaria, 
•which  were  inter  se  sifhilia,  aggregate  existences  could  only  be  discriminated 
into  hetera,  they  would  all  be  similia  and  they  could  have  but  one  compou 
name.  But  the  facial  gregaria  inter  se  differentia  are  many  and  the  differ- 
ential capacial  gregaria  are  innumerable;  and  could  we  pind  an  aggregate 
existence,  in  which  all  the  facl^  and  capacial  gregaria  exccj&ting  one  were 
.  like  those  of  gold,  yet  as  it  differed  from  gold  in  one  respect,  it  and  gold 
■would  be  differentia,  and  consequently  it  would  have  to  receive  a  name  to 
distifiguish  it  from  gold  and  other  fhings.  Common  names,  thfireforCj  are  the 
names  of  the  individual  existences  severally,  which  upon  one  and  the  same 
generalization  of  existences  are  similia  or  commensuray^ 

A  proper  name  is  the  name  given  to  a  single  existence  to  distinguish  it 
from  all  others  in  the  unive;-se.  And  it  must  be  perceived  that,  besides  the 
capaciai  gregaiium  of  animation,  which  distinguishes  animals,  animals  are 
made  up  of  various  other  gregaria,  both  facial  and  capacial,  by  which  -we 
can  easily  distinguish  them  inter  se.  And  after  that  we  have  sub-divided 
them  into  species,  we  are  still  able  to  distinguish  the  individuals  of  the  samo 
species.  Take  for  instance,  the  species  or  genus  homo,  and  after  that  wo 
have  divided  this  species  into  the  five  races,  we  can  easily  distinguish  the  in- 
dividuals of  the  same  race.  Nature  is  so  fond  of  variety  that,  in  the  largest 
cities  two  men  can'feeldom  be  found,  wl>o  are  in  all  respects  similia.  And 
this  variety  of  gregaria  outpide  oi  those  upon  which  llie  generalization,  in 
respect  to  which  men  are  similia  is  made,  enables  ui.  to  impose  witjji  effect 
proper  names  upon  individuals.  Daniel  Webster,  outside  of  tliose  gregaria 
whicK  m^de  him  and  other  men  inter  se  similia,  possessed  gregwi a  facial  a«d 
capacial,  by  which  he  could  be  distinguished  and  known  from  others.  .  City 
is  a  Common  name,  and  yet  every  city,  besides  the  juxtaposition  of  houses 
and  the  jostling  of  men,  has  other  relations  and  dissimilar  plats  and  surroimd- 


43 
ings  on  the  earth  by  which  we  may  distinguish  them  by  the  proper  names 
London,  Paris,  Philadelphia,  etc.      ' 

Correlative  names  are  the  names  of  existences  so  related  to  each  other 
that  the  mention  of  the  one  suggests  the  relation ;  as  father  and  son,  hus- 
band and  wife,  mother  and  child,  cause  and  effect,  king  and  subject,  etc. 

A  concrete  name  is  the  name  of  an  existence  grounded  in  the  ego  and 
considci-cd  with  reference  to  its  ground  in  the  ego,  or  of  an  existence  ground- 
ed in  the  non-ego  and  considered  with  Reference  to  its  ground  in  the,  non- 
ego;  in  other  words  the  existences  (for,  names  in  themselves  can  not  be  con- 
crete or  abstraqi)  distinguished  by  what  are  called  concrete  names,  have 
their  locations  in  the  ego* or  in  the  non-ego,  assigned  to  them  by  the  mind 
when  their  name  rtre  spoken,  and  therefore,  they  are  concrete;  -and  frpm  this 
circumstance  the  names  of  such  existences  are  called  concrete.  An  abstract 
name  is  the  name  of  an  existence  for  which  the  mind  assigns  no  location, 
but  merely  views  ^the  existence  sul)jectively  without 'determining  its  ground 
cither  inthe  ego  or  non-ego,  as  whiteness,  fusibility,  roundness,  etc.  The 
adjecti\ce  naii;^es  of  facial  and  capacial  gregaria,  such  as  white,  red,  sweet, 
fusible,  combustible,  conscious,  etc.,  are  geaerally  concrete;  and  when  tl^e 
existences  for  which  tliey  stand  are  to  be  viewed  in  the'  abstract,  we  change 
these  names  grammatically  into  nouns:  as  whiteness,  redness,  blackness,, 
consciousness,. etc.  We  may  however  use  abjective  names  to  denote  abstract 
existences,  as  white  is  not  black,  i.  e.,  whitenesS  is  not  blackness. 

Names  have  been  divided  into  positive  and  negative.  This  division, 
however,  is  made  altogether  from  the  combination  and  appearance  of  words] 
and  notYrom  the  func.tipns  of  words  as  names.  The  division  made  by  Aris-^' 
totle  into  defiaite  and  indefinite  is  a  much  better  one:  as  definite  white,  red, 
man,  horse,  etc. ;  indefinite  not-white,  not  red,  not  man,  etc.  Definite  names] 
then,  are  names  of  individuals  S-eparately,  or  of  the  individuals  severally  of  a 
class;  and  indefinite  itumcs  are  the  names  of  anything  not  denoted  by  the 
definite  name,  whi^h  is  always  part  of  the  word  used  as  an  indefinite  name. 
The  truth  is  that  such  'names  as  not  red,  not  man,  nothing,  non-entity/  etc.] 
can  haVe  no  existence  hi  any  language^  independent  of  propositions,' they 
spring  up  in  propositions,  and  in  order  to  i*nd.erfctand  ^hejp,  we  will  have  to 
treat  of  propositions.  There  is  also  another  set  of  names,  such  as  blind, 
mute,  deaf,  etc.,  which  have  been  called  privitives;  they  certainly  exercise 
tlie  functions  of  names,  but  we  can  understand  them  much  better  afler  hav- 
ing trcaied  of  propositions.  It  has  been  usual  with  writers  on  logic  to  treat 
explicitly  of  names  and  their  divisions,  and  we  have  said  this  much  by  a 
kind  of  duress,  although  after  names  have  been  divided  itito  names  of  hetera, 
homon,  sifiiiiia.  differentia,  commensura  and  incommcnsura,  we  dceuTthe 
other  divisions  of  no  great  importance. 


i. 


y..i^»  ^^l^i ^^  ^®^™^  necessary,  at    the  end  of  this  chapter  to  notice 

briefly,  what  we  regard  as  erroneous  in  the  chapter  on  names  in  the  work  of 
J.  btuart  -MiU  on  logic;  not  because  we  wish  to  find  fault  with   Mr  Mill 
more  than  others  but  because  Mr.  Mill  is  one  of  the  strongest  writers  upon 
logic  iiT  the  English  language,  and  the  futility  of  the  subject  is,  therefore 
best  shown  from  his  work.    On  page  eighteen,  of  the  edition  pubM*hed   by 
Harper  &  iiros.,  he  says,  "A  general  name  Is  familiarly  defined,  a  name 
which  IS  capable  of  being  truly  aflBrmed  in  the  same  sense  of  each  of  an  in- 
definite  number  of  things.    An' individual  or  singular  name,  is  a  name 
JI.^i^A''A°"i^^  capable  of  being  ,truly  affirmed  in  the  same  sense  of    one 
luininf^^f  !^T.°^>^.5  same  pafre,  '«A  general  name  is  one  which  can  be 
predicated  of  each  individual  of  a  multitude;  a  collective  name  can  not  be 
predicated  ot  each  separately,  but  only  of  all  taken  together."    Now  upon 
the  foregoing,  we  would  remark  that  a  name  can  not  be  affirmed  of   any- 

thl?^ii^''K7^''X.^''P^^?^*''^  affirmation  is  contained  in  a  proposition,  and 
that,  which  is  affirmed  in  any  proposition,  can  not  be  a  name,  as  we  wil   see 

TnH^v^ ''TW^n'^.^\*?^  propositions  in  chapters  X,  XI,  XII,  XIII,  XIV 
and  Xy.  Mr.  Mill,  m  his  explaination  of  names  has  all  the  lime  hkd  in 
llV^^hr  «^°tr^^^J^'  ^,^  '^^y  »ay.  the  universally  received  hypothesis  that,  in 

FhXnrn'^fn^.LP^^^  tT  ''  "*^'°^'^  ^'  "^^"i^d  «f  t&e  subject,  or  tha^ 

the  hing  denoted  or  connoted,  to  use  a  term  of  Mr.  Mill  and  the  schoolmen 
by  he  predicate  term  is  affirmed  or  denied  of  the  thing  denoted  or  connoted 
by  the  subject-term ;  a  theory  which  we  hope  to  be  able  to  show  hereafter  to 
be  entirely  erroneous,  and  wLicfi  has  led  M?.  Mill  and  other  eminent  write^ 
into  erroneous  conceptions  of  names.  But  again  on  the  same  page  as  ^- 
•  fore.  "A  concrete  name  is  a  name  which  stands  for  a  thing  ;  an^  abstract 
I!^Sp  J^«/«^°;«  which  stands  for  an  attribute  of   a  thing."    lid  hence  the 

hP?  .Stv*°  T'^""^^  ^^  V^^^'  '^  ^^^  ""^^  ^f  NOTHING,  unless  an  attribute 
be  a  THING  of  a  THING.  But  on  page  thirty-two  he  tells  us  that,  "When  we 
have  occasion  for  a  name  which  shall  be  capable  of  denoting  whatever 

wo?^.?fnr°°lw''l?^"^'^'^  ^'^^  non-entity  or  nothing,  there  if  .iTa  Sly  a 
word  applicable  o  the  purpose,  which  is  not  also,  and  even  more  familiarly 
taken  ma  sense,  in  which   it  denotes  only  substance^'.    But  substances   aro 

T.^\lt^r'  'r''''  f  "^"^^'  %'^'^  ^^'°i  ^'"^  '^  ^«'po^"^  ofTmusri^  said 
c^p  or«  '/^^^l"^?  ^^'^  ^''*''-    ^^^  •^^«"  we  speak  of  an  object,  or  of  a  thing 

kmror'lZfL^Zfr  '^PP^^''^  K"^'^^  ^  substance.  There  seems  to  be  ^a 
Kind  of  cpntradiction  in  using  such  an  expression  as  that  one  thine  is  mere- 
ly the  attribute  of  another  thing."  From  this,  it  seems  tharMrMilPs  defi- 
nitions of  concrete  and  abstract  names  ought  to  hav^read:  a  concrete  name 
lnd,Tn'''^*'^.'.\?^^'  for  a  substance;  aS  abstract  name  is  Tname,  wh^^^^ 
at?ribute«  .?.  tTi^".''i?^/  substance:  for,  otherwise,  if  both  substanieTand 
attr  butes  are  to  be  called  things,  then  a  concrete  name,  according  to  Mr 

foT}^eteullr^^^^^^  V^  '^''  ^^^°Se  of  words  in  his  senten?^s 

S^.*  T^nf  "^  ^^*^'  ^' White  also  is  the  name  of  a  thing,  or  rather  of  things  '» 
Mr.  Mill,  we  presume  would  not  go  so  far  as  to  call  white  a  subsUnce  bit 
would  connsider  it  rather  as  an  Wibute  of  a  substance  Yer in X^^^ 
sentence  he  tells  us  that,  "Whiteness,  again.  Is  the  name  of  a  Wality  or  at 
tribute  of  those  things"  (whites).  That  whiteness  is  the  attribute  of  wh^k 
IS  certainly  strange  enough.  But  he  would  probably  say  that  whiiene^U 
not  \^c  attribute  of  white,  but  of  white  thinL    i!^.  L7,^«"llV  !rJl^?.TJ* 


not  t^o  attribute  of  wb^^^  ^^l  =oZ^l 

d?nVtt^ean%;'^^^^^ 


:«^i  •*      *"*^-  ---  -^ ««»     If  .*vii  nrc  oav  Buuw  IS  wniic,  milK  is  wnite  linen 

18  White,  we  do  not  mean  to  be  understood  that  snow,  or  linen,  ormilk  is  a 


•  ■  ■  i5 

color.  We  mean  that  they  are  things  having  the  color"  (white  is  their  attri- 
bute). "The  reverse  is  the  case  with  the  word  whiteness;  what  we  affirm  to 
be  whiteness  is  not  snow,  but  the  color  of  snow."  Well,  whiteness  then  is 
the  name  of  the  color  of  snow,  but  such  being  the  case  what  is  white  the 
nanie*offrtien  we  ray  snow  i«  white?  It  may  be  answered  that  white  is 
the  name  of  snow  itself  and  of  all  white  things,  as  Mr.  Mill  has  said  pre- 
viously. Well  then,  if  such  be  the  case,  what  is  snow  the  name  of?  Mr 
Mill's  language  is  merely  a  jargon.  But  Mr.  Mill  proceeds  to  divide  names* 
into  connotive  and  non-connotive,  and  this  division  he  considers  of  the  most 
importance,  *'And  one  of  those  which  go  deepest  into  the  nature  of  langua""e  " 
"A  non-connative  term  is  one  which  signifies  a  subject  only,  or  an-  attribute 
only.  A  connotatu;e  term,  is  one  which  denotes  a  subject  and  implies  an 
attribute.  By  a  subject  is  here  meant,  anything  which  possesses  attributes 
Thus  John,  London,  England,  are  nanie«  which  signify  a  subject  only.  None 
of  theic  names,  therefore,  are  connotative.  But  white,  long,  virtuous,  are 
connotativc.  The  word  white  denotes  all  white  things,  as  snow,  paper'  the 
foam  of  the  sea,  etc ,  and  implies,  or  as  it  was  termed  by  the  schoolmen  con- 
notes the  attribale  whiteness.  The  word  white  is  hot  predicated  of  the  attri- 
bute, but  of  the  subjects,  snow,  etc.;  but  when  we  predicate  it  of  them  we 
imply,  or  connote  that  the  attribute  whiteness  belongs  to  them."  Now  in 
the  above  sentences,  the  misconception  of  the  .meaning  of  propositions  first 
spoken  of  by  us,  is  commingled  with  the  confusion  respecting  concrete  and 
abstract  names,  which  we  noticed  a  moment  ago.  We  do  not  wish  to  fill  our 
l>ook  w  ith  strictures  upoa  the  works  of  others,  which  is  apt  to  be  regarded 
at  best  as  gqneorious.  The  best  way  to  cure  errors  is  to  bring  forward  the 
truth  and  let  it  be  examined.  And  we  repeat  the  remark  that  all  the  flivis- 
ions  of  names,  after  that  they  have  been  divided  into  names  of  homon 
hetera,  similia,  diflereniia,  commensura  and  incommcnsura,  are  of  but  small 
iuiportancc  for  the  purposes  of  explaining  the  reasoning  processes.  These 
six  classes  lie  at  the  foundation  and  are  used  in  assisting  the  undesUnding  in 
drawing  its  conclusions;  the  other  classes  are  useful,  if  useful  at  all  merely 
for  tlie  purposes  of  distinctions  in  mentioning  things,  but  they  do  not  assist 
but  ratlier  impede,  the  progress  of  science.  * 

CHAPTER  IX. 

classification  of  niOP08ITION8. 

In  the  previous  chapters,  we  endeavored  to  obUin  classifications  of 
those  objects  with  which  we  are  familiar,  and  to  treat  of  names  used  to  mark 
and  distinguish  truths.  And  it  must  have  been  observed,  that  what  former 
writers  have  called  attributes  we  call  existences,  and  when  these  existences 
co-exist,  we  name  them  grcgaria.  Among  most  logicians,  and  especially 
among  the  schoolmen,  what  they  call  attribute*  aire  said  to  inhere  in  a  sub- 
stance. But  of  this  substance  in  which  attributes  inliere,  we  hare  not  been 
able  to  gain  any  knowledge  whatever  independent  of  the  attributes.  And  we 
regard  the  name  ATTRiBirrE  as  calculated  to  mislead,  and  therefore  we  do  not 
it  at  all.  Aad  a  substance  stripped  of  gregaria  is  unknown  to  us ;  independ- 
ent of  tlie  capacial  gregaria,  we  know  nothing  o^  the  ego,  or  of  any  mind ; 
and  stripped  of  facial  and  capacial  gregaria,  we  know  nothing  of  matter! 
And  the  gregaria,  of  which  we  know  something  directly,  may  with  as  much 


46'  # 

propriety  at  least  be  called  c«Islences,  as  those  things  which  our  Ihoughls, 
IVom  our  kuowledge  of  orcgaria,  lead  us  to  suppose  to  be  in  sonic  manner, 
we  know  not  kow,  the  Ciiuscs  between  the  ego  and  nou-ego,  of  those  gie- 
garia.  We  are  able  to  say  with  confidence  that  one  tiling  per  se  can  iTot  be  a 
cause,  i.  e ,  no  piiangc  or  eftect  can  come  out  of  it.  We  are  able  to  say  witii 
cpial  confidence  that  red,  white,  sweet,  etc.,have  not  always  been  to  us  exist- 
ences, but  that  wiih  us  they  had  a  beginning;  and  therefore  we  conclude 
that  our  mind  in  and  of  itself  must  be  something",  and  that  there  are  otlur 
somethings,  whose  relations  to  tha-niind  '  caiKse  these  existences,  which  wo 
call  red,  sweet,  etc.  '    m   ^ 

Now  when  men  were  forming  language,  they  were  endeavoring  to  dis- 
tinguish by  the  names,  which  they  hit  upon,  certain  truths  which  had  come 
to  their  minds.     But  if  their  names  do  not  point  out  clearly  to  our  minds, 
-well  defined  truths,  we  lay  them  aside  vid  endeavor  to  supply  their  places 
•Witli  more  suitable  instruments.    And   it  must  appear  evident  to  every  one 
that  had  any  person  attempted  to  compose  a  treatise  on  logic  in  the   infancy 
■  of  language,  iu-order  to  have- succeeded  in  stating  what  is  now  known  about 
it,  he  would  have  liad  to  ruu  away  ahead  of  his  generation  in  the  knowledge 
of  things,  apd  to  have  invented  and  explained   terms  which   have  cost  the 
human  intellect  ages  of  labor  to  furnish  to  us.    But  happily  for  us  the  labra- 
lorfot'  thought  has  been  vigorously  operating  for  many  a  thousand  years 
before  we  have  been  called  upon  to  enter  tile  arena  of   mind.     Instruments 
for  slampinir  truths  have  been  prepared  to  our  hand  by  nations,  each   inde- 
pendent of  the  others.    And  although  language  always  has  been  and  always 
Avill  be  behind  the  wants  of  a  people  who  push  their  inquiries-  beyond   the 
already  occupied  fields  of  knowledge;  yet  the  advance  usSually  proceeds  with 
so  gradual  a  pace,  that  ihere  is  not  much  dilficulty  usually,  in  forming  the 
language  chart  of  the  newly  discovered  territory. 

Now  in  the  prcceediug  pages,  we  endeavored  to  show  how  we  obtained 
and  classified  the  4ruths  of  which  we  treated:  we  also  applied  the  names 
used  for  distinguishing  them.  At  the  same  time,  therefore,  that  we  were 
tracing  the  processes  of  the  mind  in  gaining  knowledge,  we  were^ilso  fur- 
nishing and  setting  down  the  signs  by  which 'to  distinguish  the  knowledge 
obtained.  And  if  words,  as  it  has  been  said,  are  the  forts  established  To 
guard  and  keep  mental  ittquisitions,  we  should  expcCt  a  .writer,  who  puts  his 
truths  carefully  into. groups  for  future  use,  to  fprtify  them  witli  proper  terms, 
as  he  passed  along.  This  we  have  endeavored  to  do.ns  well  as  we  were  able ; 
and  then  we  took  a  view  of  these  names  or  forts.  We  must  proceed,  there- 
fpre,.tv:>  connect  those  names,  or  forts,' together  and  consider  the;  results!  This 
is  done  by  the  use  of  propositions. 

A  proposition,  in  general,  we  define  lo  be  the  result  of  the.^jomparison 
of  exigences  made  by.  the  mind  and   expressed  in  words;   and   under  this 


»  •    47 

general  defiuition  of  proposition  we  make  two  classes  of   propositions-? iz: 
logical   and   conclusional   propositions.    A   log'ical;  proposition   is   one  in 
uhich  llwe  result  of  the  Comparison  between  two  existences  made  immediately 
by  the  mind  is  expressed   in  words;  a  conclusioual   proposition  is   one  in 
^  which  the  comparison  between  Iwo  ormore  existences  is  mado  immediately 
*  by  means  of  a  particular  existence  or  existences  and  Uie  result  of  the  com- 
parison is  expressed  in  wftids.    The  sun  is  an  existence,  fire  burns,  snow.. is 
white,  etc.,  are  example  of  the  first  class.    In  each  of  these  propositions  there 
is  a  mental  comparison  immediately  made  between  tt*vo  existences,  and  tUo 
result  ol  the  comi^rigpu  is  exprensed  in  words.    The  expressions;  the  sun  is 
and  the  sun  is  an  existence,  arc  equivalent :  fire  burns,  is  equivalent  to  fire  js 
the-cause  of  burninjr  sensations:  fire  itself  is, the  efiect  of  chemical  aftlnities. 
And  hence  every  proposition   fujly  stated  requires  a  subject  and  predicate, 
i.e.,  .a  name  to  distinguish  the  truth  upon  which  the  mind  fim  looks,  and 
also  a  name  to  point  out  the  trutli  connected  with   th€  first  in   comparison. 
The  comparison  m^iy  frequently,  by  a  mode  of  speech,  be  expressed  by  using 
the  n:uuc  of  the  subject  only  with  a  verb:  and  in  such  cases  the  other  exis- 
tence compared  is  suggeste<i  and  compared  by  the  verb,  i.  e.,  the  verb  both 
points  out  aud  compares  the  predicate  witUthe  subjept.    This  Vis  geqenally 
tbc  case,  when  tlio«ubject  or  first  existence  considered  is  the  reputed  oftusc 
of  the  second. one:  as  fire  burns,  ice  cqoIs,  the  sun  shines,  the  n>ind  iHink-s 
etc.    Tliis  is  also  the  case  when  the  first  existence  is  looked  upon  as  thesuL- 
joct  upon  wlkieh  some  efiect  is  produced:  as  beauty  fades,  water  runs,  leaves 
fall,  etc.    But  all  such  propositions  m.iy  be  made  by  wording  them'diflfer- 
ently  to- set  out  a  subject,  a  predicate  aud  a  copula,  i.  e.,  m  each   of  which 
propositions,  two  well  denned  truths  shall  appear,  the  one  as  subject  and  tlio 
other  as  predicate,  with  a  copula  to  express  the  result  of  the  comparison. 
The  verb  used. in  our  king u age,  as  the  copula,  may  always  be  made  to  be 
some  part  of  the  substantive  verb  to  ue;  as  snow  is  whi^e. 

Kow  respecting  the  meaning  of  this  copula,  in  propositions  there  hiis 
been  much  dispute  among  authors.  When  we  say  that  the  sun  is,  we. mean 
that  thS  sun  exists,  is  an  existence,  /ibis,  indeed,  is  the  primary  meaningof 
the  verb  to  be.  But  besides  tiiis  meaning  autiftns  tell  us  that  it  has  another; 
a3  when  we  say  John  is  a  man;  they  luil  us  we  use  the  copula  is  merely  as 
the  sign  of  predication.  And  alt)iQugh  in  the  pi^oposition,  the  sun  ia,  tliey 
tell  us  18  is  a  pretiicale  of  itself,  yet  when  a  name  is  placed  after  it,  it'  theii 
passes  Us  preuicablc.qualHy  over  to  that  name.  All  this  is  certainly  some- 
what obscure.  For,  when  we  take  from  the  verb  to  be  its  primary  significa- 
tion and  cail  it  a  sign  of  predication,  what  tlo  we  mean  by  this  expression? 
We  mean,  say  our  authors,  that  the  copula  aflirms  one  tUiugpf  another.  But 
I  do  not  ace  that  any  more  4 ight  has  been  thrown  upon  the  subject,  by  the 
change  of  phraseology.    When  we  say  that  ice  is  frozijp  water,  according  to 


43- 

tklseiplainatJan,  we  afflr^  frozen  water  of  ic,  when  in  truth  ft-ozen  ^^^^^^ 
and  ice  are  the  same  tkm«,  ^d  therefore,  in  truth,  we  affirm  ,t8.lf  of    he 
subject.    Bat  if   il  be  explained  by  saying  lliat  the  copula  shows  tha    the 
subject  possesses  the  predicate,  •r  that  the  predicate  belongs  to  the  subject. 
as  It  is  usually  done,  we  answer  that  this  explaination  explains  nothing. 
For  according  to  this  doctrine,  ice  possesses  froze*  water,  or  frozen  wirier 
belJngsto  U^etamere  jagon  of  words.    But  it  is  said  ;«That  the  ernploy- 
ment  of  it  (the  copula)  a»  a  copula  does  not  necessarily  include  the  affirma- 
tion of  existence  appears  from  such  a  proposition  as  this,  »A  centaur  is  a 
flctioD  of   the  poets.'  where  il  can  not  possibly  be  m^fhled  that   a  centaur 
exists,  sinee  the  proposition   itself  expressly  asserts,  llmt  the  thing  has  no 
real  existence."-J.  Stuart  Mill.    To  this  we  answer,  that  a  cenUur  has  areal 
existence,  nor  does  the  proposition  assert  the  contrary.    Its  existence,  how- 
ever, is  grounded  in  the  cg«.  as  the  proposition  asserts,  "A  fiction  of  the 
poets."    Although  modern  logicians  have  arrived  at  more  certain  conclusions, 
io  very  many  respects,  yet  in  their  expositions  of  propositions,  they  are  as 
much  at  lault  as  the  ancients.    TXve  truth  is  that  the  verb  to  be  as  the  copula 
in  propositions,  maintains  its  primitive  meaning  in  every  Instance,  nor  can  it 
be  shown  to  have  any  other  4n  any  case.    We  may.  Indeed,  say  that  it  is 
merely  the  sign  of  predication,  but  when  we  come  to  •xamine  closely  Ihis 
expression,  we  will  lind  it  to  be  merely  words  without  knowledge.    Such 
expressions  as  these,  snow  is  white,  John  is  a  man.  leaves  arc  green,  etc.. 
were  brought  into  use  before  philosophy  had  made  a  beginning;  they  are 
natural,  short  and  convenient  modes  ef  expression  and  explicit  enough  for 
the  wants  of  mankind  in  communicating  thought  in  a  general  manner;  the 
philosophic  interpretation  of  them,  however,  by  writers  upon  logic,  we  re- 
gard as  erroneous,    iiut  wc  must  defer  the  further  consideration  of  the  copula 
until  we  come  to  the  interpretation  of  propositions,  when  we  hope  to  give  a 
full  and  clear  explainalion  of  the  whole  matter;  and  we  have  merely  advert- 
ed to  the  subject  here,  for  the  sake  of  order,  and  to  put  the  reader  on  his 
guard  against  what  we  consider  errors. 

From  the  supposition  that  in  all  propositions  there  is  something 
affirmed  of  llie  subject  io  c^tain  cases,  and  something  denied  of  the  sub- 
ject in  other  cases,  writers  l>ave  classified  propositions  into  affirmative  and 
negative.  But  this  classiflcation,  in  our  view,  is  unscientific  and  built  upon 
a  sandy  foundation.  Every  proposition,  indeed,  expresses  a  discourse  of  the 
mind,  which  may  be  denied  or  contradicted.  But  if  we  place  before  our 
m4cd  a  single  existence  either  simple  or  aggregate,  red  for  instance,  as  the 
subject  of  every  proposition  must  be,  we  can  deny  nothing  of  that  existence: 
if  we  say  anything  at  all  about  it,  we  must  make  an  affirmation.  Take  the 
two  propositions,  John  is  well,  and,  John  Is  not  well:  and  if  we  consider  the 
one  as  a  reply  to  th«  other,  there  will,  indeed,  l)e  a  denial ;  JhU  coDtemplatitig 


^  '49 

either  one  of  them  as  indepeadent  of  the  other,  and  it  contains  an  affirma- 
tion. And  further,  if  this  appear  obscure,  we  may  ask  ourselves,  whether 
both  expressions  are  really  propositions,  and  if  they  are,  then  they  must  have 
something  in  common:  proposition  must  be  the  genus  of  which  each  is  a 
species.  If  they  be  differentia,  and  yet  in  some  generalization  similia,  they 
must  have  been  differentiated  from  the  higher  class  in  which  they  were 
similia.  But  if  we  say  that  the  ene  affirms  something  of  something,  and  the 
other  denies  something  of  something,  as  is  done,  they  then  have  nothing  in 
common,  excepting  that  each  has  a  subject  and  a  predicate,  i.  e.,  one  existence 
before  and  another  aften  the  copula.  But  if  the  names  of  the  two  existences 
compared  in  propositions  be  set  down,  as  may  always  be  done,  and  we  dis- 
tinguish the  one  from  the  other  by  calling  the  one  the  subject  and  the  other 
the  predicate,  this  is  merely  a  classification  of  the  terms,  and  terms  alone  do 
make  a  proposition.  The  classification  of  terms,  therefore,  can  not  be  the 
thing  in  common,  which  unites  all  propositions  in  a  common  class.  But  if 
some  propositions  affirm  and  others  deny,  these  things  (affirmation  and  de- 
nial) are  differentia,  and  there  is  nothing  left  in  which  the  propositions  can 
agree  excepting  the  classification  of  terms.  In  the  two  propositions  "A  pear 
is  a  fruit,"  and,  *'An  apple  is  not  a  pear,"  we  consider  that  there  is  no  denial 
in  either  case,  both  are  affirmations ;  though  this  doctrine  will,  no  doubt, 
sound  strange  to  those  inaoctrinated  from  the  books  upon  logic.  They 
affirm,  however,  results  which  inter  se  are  differentia.  This  doctrine  will  bo 
easily  understood  after  that  we  have  treated  of  the  interpretation  of  propo- 
sitions. 

What  .we  consider,  therefore,  the  proper  mode  of  classifying  proposi- 
tions is  by  the  differentiating  of  the  results  affirmed.  We  dedned  a  logic^ 
proposition  to  be  the  result  oT  a  comparison  made  immediately  by  the  mind 
between  two  existences  expressed,  or  aflirmed,  in  words.  Affirmation,  we 
consider,  is  the  very  thing  in  common  in  all  propositions;  but  the  results 
affirmed  are  differentia.  And  these  results,  we  find,  may  be  discriminated 
into  six  classes,  and  therefore,  we  make  six  classes  of  propositions,  viz : 
homonical,  heterical,  similical,  differential,  commensural  and  incommensural 
propositions.  It  is  not  necessary  that  we  should  take  up  each  of  these  classes 
and  give  them  further  attention  here;  for  we  are  only  classifying  preparatory 
to  a  thorough  investigation  hereafter.  Some  things  have  to  be  merely  stated 
at  first,  so  that  the  explainatioa  when  it  coi^es,  may  be  understood. 

Now  each  of  the  above  classes  might,  apparently,  be  subclassified  into 
aimple  and  complex  propositions.  A  simple  proposition;  then,  would  be  one 
in  which  one  subject  is  compared  with  one  predicate,  as  "John  is  a  boy." 
And  a  complex  proposition  would  be  onf  in  which  one  and  the  same  subject 
is  compared  with  each  of  two  or  more  predicates;  or  in  which  one  and  the 
smm  predicate  is  compared  with  each  of  two  or  more  subjects;  or  in  which 


tMseiplalnallon,  we  affiri^  frozen  water  of  ice  when  ^-^'^^'^J'l^^ 
and  ice  are  the  same  tkiog,  and  therefore,  in  truth  we  affirm    «elf  of  the 
sobjecl     But  if   it  be  explained  by  saying  that  the  copula  *1>«^»  ^^*J^/^f 
?£  p---a  the  predicate,  •r  that  the  predicate  belongs  to  the  sUb  aet. 
a.  It  is  usually  done,  we  answer  that  this  explaination  explains  nothing. 
For,  according  to  this  doctrine,  ice  possesses  frozen  water  or  frozen  w^r 
Lungs  to  icet^a  mere  Jagon  of  words.    But  it  is  said  ;'That  the  employ- 
ment of  it  (the  copula)  at  a  copula  does  not  '«^.^«'*"»^.;;"^^",^;;J^^,  "f  .^T 
tion  of  exiatence  appears  from  such  a  proposition  as  this.  *A  centaur  is  a 
fiction  of   the  poets.'  where  it  can  not  possibly  be  Uniflied  that   a  centaur 
exists,  since  the  proposition   itself  expressly  asserts,  llmt  the  thing  baa  no 
real  existence."- J.  Stuart  Mill.    To  this  we  answer,  that  a  cenUur  has  a  real 
existence,  nor  does  the  proposition  assert  the  contrary.    Its  existence,  how- 
ever, is  grounded  in  the  ego.  as  the  proposition  asserts.  "A  fiction  of  the 
poets."    Although  modern  logicians  have  arrived  at  more  certain  conclusions, 
io  very  many  respects,  yet  in  their  expositions  of  propositions,  they  are  as 
»ucb  at  fault  as  the  ancients.    The  truth  is  that  the  verb  to  be  as  the  copula 
in  propositions,  maintains  its  primitive  meaning  in  every  instance,  nor  can  it 
be  shown  to  have  any  other  in  any  caee.    We  may.  indeed,  say  that  it  is 
merely  the  sign  of  predication,  but  when  we  come  to  oxamine  c  osely  Ihis 
expression,  we  will  find  it  to  be  merely  word,  without  knowledge.    Such 
expressions  as  these,  snow  is  white,  John  is  a  man.  leaves  arc  green,  etc.. 
were  brought  into  use  before  philosophy  had  made  a  beginning;  they  are 
natural,  short  and  convenient  modes  ef  expression  and  explicit  enough  for 
the  wants  of  mankind  in  communicating  thought  in  a  general  manner;  the 
philosophic  interpretation  of  them,  however,  by  writers  upon  logic,  we  re- 
gard as  erroneous.    But  wc  must  defer  the  further  consideration  of  the  copula 
until  we  come  to  the  interpretation  of  propositions,  when  we  hope  to  give  a 
full  and  clear  explainalion  of  the  whole  matter ;  and  we  have  merely  advert- 
ed to  the  subject  here,  for  the  sake  of  order,  and  to  put  the  reader  on  his 
guard  against  what  we  consider  errors. 

From  the  supposition  that  in  all  propoaltlons  there  is  something 
affirmed  of  the  subject  io  c^tain  cases,  and  something  denietl  of  the  sub- 
ject in  other  cases,  writers  Ivave  classified  propositions  into  affirmative  and 
negative.  But  this  classification,  in  our  view,  is  unscientific  and  built  upon 
a  sandy  foundation.  Every  proposition,  indeed,  expresses  a  discourse  of  the 
mind.  wWch  may  be  denied  or  contradicted.  But  if  we  place  before  our 
mlcd  a  single  existence  either  simple  or  aggregate,  red  tor  instance,  as  the 
subject  of  every  proposition  mutt  be.  we  can  deny  nothing  of  that  existenec: 
if  we  say  anything  at  all  about  it.  we  must  make  an  affirmation.  Take  the 
two  propositions,  John  is  well,  and,  John  is  not  well :  and  if  we  consider  the 
one  as  a  reply  to  th«  other,  there  will,  indeed,  be  a  denial ;  IhU  contemplating 


>  '49 

either  one  of  them  as  independent  of  the  other,  and  it  contains  an  affirma- 
tion. And  ftirther,  if  this  appear  obscure,  we  may  ask  ourselves,  whether 
both  expressions  are  really  propositions,  and  if  they  are,  then  they  must  have 
something  in  common :  proposition  must  be  the  genus  of  which  each  is  a 
species.  If  they  be  differentia,  and  yet  In  some  generalization  similia,  they 
muBt  have  been  differentiated  from  the  higher  class  in  which  they  were 
similia.  But  if  we  say  that  the  ene  affirms  something  of  something,  and  the 
other  denies  something  of  something,  as  is  done,  they  then  have  nothing  in 
common,  excepting  that  each  has  a  subject  and  a  predicate,  i.  e.,  one  existence 
before  and  another  aflen  the  copula.  But  if  the  names  of  the  two  existences 
compared  in  propositions  be  set  down,  as  may  always  be  done,  and  we  dis- 
tinguish the  one  from  the  other  by  calling  the  one  the  subject  and  the  other 
the  predicate,  this  is  merely  a  classification  of  the  terms,  and  terms  alone  do 
make  a  proposition.  The  classification  of  terms,  therefore,  can  not  be  the 
thing  in  common,  which  unites  all  propositions  in  a  common  class.  But  if 
some  propositions  affirm  and  others  deny,  these  things  (affirmation  and  de- 
nial) are  differentia,  and  there  is  nothing  left  in  which  the  propositions  can 
agree  excepting  the  classification  of  terms.  In  the  two  propositions  "A  pear 
is  a  fruit,"  and,  ''An  apple  is  not  a  pear,"  we  consider  that  there  is  no  denial 
in  either  case,  both  are  affirmations ;  though  this  doctrine  will,  no  doubt, 
sound  strange  to  those  inaoctrinated  from  the  books  upon  logic.  They 
affirm,  however,  results  which  inter  se  are  differentia.  This  doctrine  will  be 
easily  understood  after  that  we  have  treated  of  the  interpretation  of  propo- 
sitions. 

What  .we  consider,  therefore,  the  proper  mode  of  classifying  proposi- 
tions is  by  the  differentiating  of  the  results  affirmed.  We  defined  a  logic^ 
proposition  to  be  the  result  of  a  comparison  made  immediately  by  the  mind 
between  two  existences  expressed,  or  affirmed,  in  words.  Affirmation,  we 
consider,  is  the  very  thing  in  common  in  all  propositions;  but  the  results 
affirmed  are  differentia.  And  these  results,  we  find,  may  be  discriminated 
into  six  classes,  and  therefore,  we  make  six  classes  of  propositions,  viz : 
homonical.  hetcrical,  similical,  differential,  commensural  and  incommensural 
propositions.  It  is  not  necessary  that  we  should  take  up  each  of  these  classes 
and  give  them  further  attention  here;  for  we  are  only  classifying  preparatoiy 
to  a  thorough  investigation  hereafter.  Some  things  have  to  be  merely  stated 
at  first,  so  that  the  explaination  when  it  copies,  may  be  understood. 

Now  each  of  the  above  classes  might,  apparently,  be  subclassified  into 
simple  and  complex  propositions.  A  simple  proposition,'  then,  would  be  one 
in  which  one  subject  is  compared  with  one  predicate,  as  "John  is  a  boy." 
And  a  complex  proposition  would  be  on/i  in  which  one  and  the  same  subject 
is  compared  with  each  of  two  or  more  predicates;  or  in  which  one  and  the 
Mun^redicate  is  compared  with  each  of  two  or  more  subjects;  or  in  which 


50 
two  or  more  subjects  are  compared  with  two  or  more  predicate!.  What,  how- 
ever, is  called  a  complex  proposition  is  really  a  single  propoBition  expressed 
and  one  or  more  others  understood,  as  "John  is  good  and  wise,"  equivalent 
to  "John  is  good  and  John  is  wise."  Again,  "John  and  James  are  good  and 
■wise,"  is  equivalent  to  "John  is  good  and  John  is  wise  and  James  is  good  and 
James  is  wise."  "John  is  not  good,"  is  a  simple  proposition  of  a  different 
kind,  and  "John  is  neither  good  nor  wise,"  is  a  complex  proposition  of  ffee 
same  kind.  And  "All  the  Apostles  were  Jews,"  "All  the  boys  in  the  house 
are  barefooted,"  etc.,  are  complex  propositions.  The  classification  of  propo- 
sitions into  simple  and  complex,  however,  is  not  a  classification  of  propo- 
sitions, as  such,  but  rather  a  division  of  them  according  to  the  number  of 
propositions  expressed  and  employed  in  a  set  of   words  which  contain  but 

one  verb. 

But  again,  propositions  have  been  divided  into  pure  and  modal,  as 
"Brutus  killed  Ca?sar,"  (pure)  and  "Brutus  killed  Caesar  justly"  (a  modal 
proposition).  This  division  of  propositions  is  made  merely  from  the  appear- 
ance given  to  propositions  by  the  wording  of  them,  and  it  is  not  a  division 
of  propositions,  as  such,  at  all.  The  sentence  "Brutus  killed  Cicsar  justly," 
contains  a  result  which  will  be  exactly  expressed  by  another  set  of  words,  as 
**Th€  killing  of  Coesar  by  Brutus  was  just";  a  pure  proposition.  The  divis- 
ion has  no  foundation,  whatever,  in  the  nature  of  propositions,  but  rests  en- 
tirely upon  the  wording  of  them. 

But  again,  propositions  have  been  divided  into  univ(*rsal  or  general,  as 
"All  men  are  mortal";  particular,  "John  is  mortal";  individual  or  singular, 
"A  man  is  mortal" ;  and  indefinite,  "Some  men  are  strong".  We,  however, 
reject  these  divisions,  as  divisions  of  propositions,  as  such.  The  words  Ai*l, 
EVERY,  SOME,  etc,  jolncd  to  subjects  or  predicates  qualify  them  and  make 
Ihem  a  certain  kind  ©f  subjects  and  predicates,  but  the  aftlrmalions  is  made  in 
Buch  propositions,  just  as  it  is,  where  these  wortls  are  wanting.  These  words, 
therefore,  qualify  the  results  of  comparisons  only  by  their  qualifying  effect 
upon  the  existences  compared  in  propositions,  the  manner  of  making  the 
affinnation  is  iu  no  way  affected  by  them ;  thfy  belong  to  subjects  and  predi- 
cates and  not  to  the  result  affirmed  which  is  the  essence  of  propositions. 

The  sub-classification  therefore,  which  we  will  make,  is  into  categori- 
cal and  hypothetical  propositions.  A  categorical  proposition  is  one  in  which 
ji  certain  result  is  expressed  as  actually  existing  in  the  relation  of  existences, 
as  RED  is  a  color,  red  is  not  green,  etc.  An  hypothetical  proposition  is  one 
iu  which  a  certain  result  is  supposed  to  exist  in  the  relation  of  existences, 
for  the  purpose  of  drawing  some  conclusion  from  it;  as  "If  a  sheep  be  a 
horse,  (hypothetical)  a  lumb  is  a  colt"  (conclusion).  This  wh#le  phrase 
would  be  considered  hypothetical  by  writers  upon  logic.  Tlie  hjTiothesis, 
howe\'er,  lies  in  the  first  proposition,  "If  a  sheep  be  a  horse,"  the  latter  «en- 


51 
teuce  is  not  hvpotl.etica),  but  a  categorical  conclusion,  which  cxpressee  a 
result  flowing  actually  from  the  hypothesis;  but  the  hypothesis  being  false 
the  conclusion  dcpenJing  upon  it  must  be  false  also. 

Now  before  leaving  logical  propositions,  we  must  say  a  few  things 
about  subjects  and  predicates.  Subjects  may  be  divided  into  simple  and 
aggregate.  A  simple  subject  is  a  single  existence  per  se,  as  "Red  is  not 
gseen,"  here  red  is  a  simple  primary  propositional  truth.  An  aggregate  sub- 
ject is  an  aggregate  existence,  as  "Iron  is  hard."  Here  iron  is  an  aggregate 
existence  made  up  of  certain  facial  and  capacial  grepari a  entering  into  a 
kind  of  fasciculus,  which  gi*egaria  are  the  things  in  fasciculo  for  which  the 
subjective  term  stands  and  which  it  distinguishes.  Predicates  are  divided  in 
like  manner.  This  is  all  that  we  need  say  at  present  respecting  subjects  and 
predicates:  when  we  come  to  unravel  the  meanings  of  propositions,  we  will 
liave  to  consider  subjects  and  predicates  more  fully.  And  this  brings  us  to 
notice  logical  conclusions,  or  conclusional  propositions,  about  which  we  will 
say  but  little  at  present  as  they  will  be  treated  again  hereafter. 

A  logical  or  ratiocinitive  conclusion,  as  already  said,  is  a  proposition 
in  which  the  result  of  comparisons  mediately  made  by  means  ol  certain  ex- 
istences, is  expressed  in  words.  In  a  logical  proposition  the  result  of  the 
comparison  made  immediately  between  two  existences  is  expressed  in  words f 
but  in  a  conclusional  proposition  thercsult  is  not  derived  from  the  immediate 
comparison  of  two  existences,  but  mediately,  as  A  is  equal  to  B,  C  is  equal  to 
A,  and  therefore  C  is  equal  to  B  (a  conclusion).  In  the  last  proposition, 
which  is  a  conclusion,  the  comparison  between  C  and  B.isnot  immediate,  but 
mediate  by  the  means  ol  A.  This  distinction  between  logical  propositions 
aild  conclusional  propositions  is  important  to  the  clear  understanding  of 
logic:  for  it  is  evident  that  a  conclugion  once  gained  may  be  made  the 
premise  in  a  subsequent  syllogism,  and  unless  we  understand  this  distinction, 
we  will  not  know  how  to  get  to  the  bottom  of  the  reasoning  process. 

All  those  propositions  which  have  been  denominated  modal,  by  writers 
are  conclusional  propositions,  as  "Brutus  killed  Ca?sar  justly"  is  a  conclusion! 
And  much  of  what  we  have  already'  said  about  logical  jpropositiona,  will 
apply  to  conclusional  propositions,  we  need  not  therefore,  repeat  it.  Propo- 
sitions, which  are  called  disjunctive,  ali^o,  arenot  logical  propositions  proper, 
but  conclusions,  the  premises  of  which  are  often  not  mentioned:  as  "John  is 
either  a  knave  or  a  fool,"  is  not  properly  a  logical  proposition,  but  a  conclu- 
sion drawn  from  some  premises,  which  are  found  in  and  can  be  made  out  of 
John's  actions.  What  have  been  called  hypothetico  disjunctive  or  dilematic 
propositions,  also,  are  cooclusious,  as  we  will  more  fully  see  and  explain 
hereafter. 

In  this  chapter  we  have  endeavored  to  classify  propositions  so  that  we 
may  be  more  ea.?ily  understood  in  our  subsequent  inquiries.    All  truths,  and 


53 

I  especially  those  about  logic,  are  so  interlinked  that  we  are  obliged  to  draw, 
sometimes,  upon  those  whose  explaination  has  not  yet  been  given  in  order  to 
accomplish  the  work  on  hand.    And  the  subject  upon  which  we  have  been 

^  engaged  and  which  we  must  yet  consider  more  closely,  has  been  misunder- 
stood, as  we  believe,  by  all  writers  heretofore  upon  logic. 

I 

I  CHAPTER  X. 

!  HOMONICAL  PROPOSITIONS. 

j  We  have  defined  a  logical  proposition  to  be  the  result  of  a  comparison 

between  two  existences  made  immediately  by  the  mind  and  expressed  in 
words:  and  a  conclusional  proposition  to  be  the  result  of  comparisons  be- 
tween existences  made  mediately  and  expressed  in  words.  We  will  first  give 
pur  attention  to  logical  propositions.    And  the  result  expressed  in  every  legi- 

'  cal  proposition  will  be  either  a  truth  or  an  error.    If  our  faculties  be  in  a 

perfect  state  and  exercised  in  the  right  manner,  the  result  will  generally  be  a 
truth :  but  if  our  faculties  do  not  act  in  a  legitimate  and  sufllciently  vigorous 
manner,  we  will  obtain  an  error.  In  every  instance,  therefore,  it  is  always 
necessary,  in  order  to  obtain  a  truth  by  comparison,  that  we  should  have  an 
adequate  knowledge  of  each  of  the  two  truths  compared  in  logical  proposi- 
tions. We  have  already  shown  that  all  existences  may  be  compared  one  with 
another,  and  that  knowledge  is  a  result  brought  out  of  the  relations  oL  exis- 
tences. To  show,  indeed,  how  the  mind  possesses  the  capacity  in  itself  to 
compare  is  no  part  of  our  undertaking;  but  that  it  actually  does  compare 
among  tlie  existences  which  are  the  subjects  of  its  cognitions,  and  hence 

i  gain  knowledge  by  the  comparisons,  we  think,  has  been  sufficiently  shown 

]  already. 

j  Now  when  the  mind  has  gained  knowledge  and  clothed  this  knowledge 

with  words,  i.  e.,  given  it  as  it  were,  a  body  to  render  it  visible  to  others,  Ih© 
knowledge  gained,  indeed,  is  thus  made  appreciable  to  others,  but  the  opem- 
tions  of  the  mind  in  gaining  that  knowledge,  leave  no  trace  behind.  And 
did  every  proposition  clearly  exhibit  the  two  existences  compared,  and  also 
the  result  or  truth  gained  by  their  comparison,  propositions  would  need  no 
interpretation,  for  each  one  would  fully  interpret  itself.  But  Ihe  men  who 
commenced  language,  were  seeking  merely  for  an  instrument  of  utiliry^  in 
the  common  affairs  of  their  lives,  in  which  clearness  of  detail  and  precision 

,  of  expression  were  of  less  importance  than  general  availability  and  dispatch. 

And  therefore,  in  every  language,  the  truths  which  are  really  compared  in 
propositions  ai-e  sometimes  but  dimly  shadowed  forth,  and  the  result  of  their 

,  comparison  always  but  obscurely  shown  by  the  form  of  the  words.    And  this 

N  makes  it  necessary,  in  order  to  obtain  a  thorough  insight  into  propositions, 

to  show  what  the  two  truths  compared  really  are,  that  the  result  of  their  com- 

'  parlson  may  be  clearly  perceived.    To  this  task,  therefore,  we  now  proceed; 


and  we  will  comineucc  with  the  cxamiaation  of  homoaical   propositions. 

Take  the  proposition  "Ked  is  red,"  and  let  us  endeavor  to  clearly  set 
out  the  two  things  compared  and  the  truth,  which  is  the  result  of  their  com- 
]  arison.  And  fir«t,  we  must  observe  that  an  existence  which  is  absolutely' 
the  same  existence  can  not  be  two  existences,  and  that  one  thinf,  per  se  can 
not  be  comparcd^at  all :  two  existences  must  always  be  found  in  every  propo- 
sition. We  must  also  observe  that  when  we  have  the  knowledge  of  an  exis- 
tence, we  can  always  make  some  discrimination  respecting  that  existence:  for 
wiihont  some  discrimination  we  can  have  no  knowledii^e.  Plurality  of  ex- 
istences is  necessary  to  our  knowledge  of  anyone;  and,  tkerefore,  absolute 
oneness  or  identity  is  not  within  our  knowledj^e:  every  truth  of  which  we 
have  any  knowledge  is  evolved  from  relations.  I3ut  how  then  can  we  say 
that  "John  is  John,"  or  what  is  equivalent  to  this,  "John  is  himself"?  In 
order  to  understand  this  it  is  necessary  to  recollect  that  some  truths  ara 
•2:rounded  in  the  non-ego  and  others  in  the  ego.  It  we  look  at  a  tree,  the  relations 
between  the  tree  and  the  ego  bring  to  our  knowledge  an  existence  (a  tree) 
grounded  in  the  non-ego,  and  also  an  int(;rnal  existence  grounded  in  the  ego. 
Now  simple  existences  can  only  be  discriminated  by  their  wheres,  by  their 
times  and  by  their  effects.  Many  effects  upon  the  mind  are  inter  se  similia; 
thus  if  we  look  at  an  inkstand  to-day,  and  to-morrow  look  at  it  ao-ain :  both* 
to-day  and  to  morrow  it  will  produce  etlects  upon  the  mind  exactly  similar^ 
yet  these  effects  will  not  be  the  same,  they  will  not  be  homon,  for  they  can  be 
discriminated  by  their  times.  But  similar  effects  upon  our  minds  can  only 
be  discriminated  by  their  times:  and  where  there  can  be  no  hetcration  of 
times  made,  there  can  be  but  one  and  the  same  existence  grounded  in  tlio 
ego,  similarity  is  lost  in  identity.  And  we  must  always  recollect  that  by  the 
ego,  we  mean  my  mind  for  me  and  your  mind  for  you:  For  should  I  and  a 
thousand  other  persons,  at  one  and  at  the  same  iilstaut  of  time,  look  at  an 
object  and  be  affected  by  itx'xactly  alike,  3'et  to  n\e  only  one  of  these  effects 
would  be  gfbunded  in  the  ego:  and  all  the  efl'ects  upon  the  minds  of  the 
others  in  respect  to  myselt  would  be  grounded  in  the  non-ego.  Similar 
tfuths,  therefore,  grounded  in  the  ego,  which  can  not  be  differentiated,  but 
whose  times  can  be  heterated,  are  not  one  and  the  same,  but  separate  exist- 
ences: they  are  hetera.  But  with  respect  to  truths  grounded  in  the  non-e^o, 
though  their  effects  upon  the  mind  may  be  exactly  similar,  or  to  change  the 
form  of  expression,  these  truths  may  exactly  resemble  each  other,  yet  if  their  , 
WHERES  can  be  heterated,  they  are  not  the  same  but  separate  existences.  If 
three  men  receive  mental  impressions  exactly  similar,  yet  any  person  can 
heterate  the  wheres  of  these  effects  and  therefore  the  effects  are  not  the  same. 
Dissimilar  truths  grounded  in  the  non-ego,  or  in  the  ego,  can  be  discrimi- 
nated into  differentia,  they  can  be  differentiated ;  but  similar  truths  grounded 
in  the  non-^go,  whose  wheres  cftn  not  be  heterated,  are  to  us  the  same.    It 


53 

especially  those  about  logic,  are  so  interlinked  that  we  arc  obliged  to  draw, 
sometimes,  upon  those  whose  explaination  has  not  yet  been  given  in  order  to 
accomplish  the  work  on  hand.  And  the  subject  upon  which  we  have  been 
engaged  and  which  we  must  yet  consider  more  closely,  has  been  misunder- 
stood, as  we  believe,  by  all  writers  heretofore  upon  logic. 

CHAPTER  X. 

HOMONICAL  PROPOSITIONS. 

We  have  defined  a  logical  proposition  to  be  the  result  of  a  comparison 
between  two  existences  made  immediately  by  the  mind  and  expressed  in 
words:  and  a  conclusional  proposition  to  be  the  result  of  comparisons  be- 
tween existences  made  mediately  and  expressed  in  words.  We  will  first  give 
pur  attention  to  logical  propositions.  And  the  result  exprifssed  in  every  logi- 
cal proposition  will  be  either  a  truth  or  an  error.  If  our  faculties  be  in  a 
perfect  state  and  exercised  in  the  right  manner,  the  result  will  generally  be  a 
truth :  but  if  our  faculties  do  not  act  in  a  legitimate  and  sufficiently  vigorous 
manner,  we  will  obtain  an  error.  In  every  instance,  therefore,  it  is  always 
necessary,  in  order  to  obtain  a  truth  by  comparison,  that  we  should  have  an 
adequate  knowledge  of  each  of  the  two  truths  compared  in  logical  proposi- 
tions. We  have  already  shown  that  all  existences  may  be  compared  one  with 
another,  and  that  knowledge  is  a  result  brought  out  of  the  relations  ot  exis- 
tences. To  show,  indeed,  how  the  mind  possesses  the  capacity  in  itself  to 
compare  is  no  part  of  our  undertaking;  but  that  It  actually  does  compare 
among  the  existences  which  are  the  subjects  of  its  cognitions,  and  hence 
gain  knowledge  by  the  comparisons,  we  think,  has  been  sufficiently  shown 
already. 

Now  when  the  mind  has  gained  knowledge  and  clothed  this  knowledge 
with  words,  i.  e.,  given  it  as  it  were,  a  body  to  render  it  visible  to  others,  the 
knowledge  gained,  indeed,  is  thus  made  appreciable  to  others,  but  the  opem- 
tions  of  the  mind  in  gaining  that  knowledge,  leave  no  trace  behind.  And 
did  every  proposition  clearly  exhibit  the  two  existences  compared,  and  also 
the  result  or  truth  gained  by  their  comparison,  propositions  would  need  no 
interpretation,  for  each  one  would  fully  interpret  itself.  But  the  men  who 
commenced  language,  were  seeking  merely  for  an  instrument  of  utility  in 
the  common  affairs  of  their  lives,  in  which  clearness  of  detail  and  precision 
of  expression  were  of  less  importance  than  general  availability  and  dispatch. 
And  therefore,  in  every  language,  the  truths  which  are  really  compared  in 
propositions  are  sometimes  but  dimly  shadowed  forth,  and  the  result  of  their 
comparison  always  but  obscurely  shown  by  the  form  of  the  words.  And  this 
makes  it  necessary,  in  order  to  obtain  a  thorough  insight  into  propositions, 
to  show  what  the  two  truths  compared  really  are,  that  the  result  of  their  com- 
parison may  be  clearly  perceived.    To  this  task,  therefore,  we  now  proceed; 


03 
md  we  will  commence  with  tlie  cxamiualion  of  homonical   propositions. 

Take  the  proposition  '*Ked  is  red,"  and  let  us  endeavor  to  clearly  set 
tut  the  two  things  compared  and  the  truth,  which  is  the  result  of  their  com- 
arison.    And  fii«t,  we  must  observe  that  an  existence  which  is  absolutely 
the  same  existence  can  not  be  two  existences,  and  that  one  Ihinf,  per  se  can 
not  be  compared^at  all :  two  existences  must  always  be  found  in  every  propo- 
sition.    Wc  must  also  observe  that  when  we  have  the  knowledge  of  an  exis- 
tence, we  can  always  make  some  discrimination  respecting  that  existence:  for 
without  some  discrimination  we  can  have  no  knowledge.    Plurality  of  ex- 
istences is  necessary  to  our  knowledge  of  anyone;  and,  tkerefore,  absolute 
oneness  or  identity  is  not  within  our  knowledge:  every  truth  of  which   we 
have  any  knowledge  is  evolved  from  relations,    liot  how  then  can  we  say 
that  "John  is  John,"  or  what  is  eqtiivalent  to  this,  "John   is  himself"?    In 
order  to  understand  this  it  is  necessary  to  recollect  that  some   trutlis   ara 
grounded  in  the  non-ego  and  others  in  the  ego.  It  we  look  at  a  tree,  the  relations 
between  the  tree  and   the  ego   bring  to  our  knowledge  an   existence   (a  tree) 
grounded  in  the  non-ego,  and  also  an  int(;rnal  existence  grounded  in  the  ego. 
Now  simple  existences  can  only  be  discriminated  by  their  wheres,  by  their 
times  and  by  their  effects.    Many  effects  upon  the  mind  are  inter  se  similia; 
thus  if  we  look  at  an  inkstand  to-day,  and  to-morrow  lo^ok  at  it  again ;  both' 
to-day  and  to  morrow  it  will  produce  effects  upon  the  mind  exactly  similai* 
yet  these  effects  will  not  be  the  same,  they  will  not  be  homon,  for  they  can  be 
discriminated  by  their  times.     But  similar  effects  upon  our  minds  can   only 
be  discriminated  by  their  times:  and  where  there  can  be  no  heteratiou   of 
times  made,  there  can   be  but  one  and  the  same  existence  grounded  in   the 
ego,  similarity  is  lost  in  identity.    And  we  must  always  recollect  that  by  the 
ego,  we  mean  my  mind  for  me  and  your  mind  for  j-ou:    For  should   I  and   a 
thousand  other  persons,  at  one  and  at  the  same  iilstant  of   time,  look  at  an 
object  and  be  affected  by  it  exactly  alike,  yet  to  n\e  only  one  of  these  effects 
would  be  gfbunded  in  the  ego:  and   all  the  eftects  upon  the  minds  of   the 
others  in  respect  to  myselt    would    be  grounded    in   the   non-ego.     Similar 
(tilths,  therefore,  grounded  in  the  ego,  which  can  not  be  differentiated,  but 
whose  times  can  be  heterated,  are  not  one  and  the  same,  but  separate  exist- 
ences: they  are  hetera.     But  with  respect  to  truths  grounded  in  the  non-e^o, 
though  their  effects  upon  the  mind  may  be  exactly  similar,  or  to  change  the 
form  of  expression,  these  truths  may  exactly  resemble  each  other,  yet  if  their  , 
WHERES  can  be  heterated,  they  are  not  the  same  but  separate  existences.     If  ' 
three  men  receive  mental   impressions  exacily  similar,  yet  any  person   can 
heterate  the  wheres  of  these  effects  and  therefore  the  effects  are  not  the  same. 
Dissimilar  truths  grounded  in  the  non-ego,  or  in  the  ego,  can  be  discrimi- 
nated into  differentia,  they  can  be  differentiated ;  but  similar  truths  grounded 
in  the  non-%o,  whose  wheres  cftn  not  be  heterated,  are  to  us  the  same.    It 


we  should  see  a  rock  of  a  particular  shape  and  color  to-day  iuone  place,  and 
to-morrow  see  a  rock  exactly  similar  in  another  place,  the  only  thing  whicii 
would  enable  us  to  know  that  these  two  rocks  are  not  the  same,  is  that  their 
present  wheres  are  hetera.  If  we  should  find  out  that  tht  first  rock  was  no 
longer  in  its  wonted  place,  and  we  could  not  tell  the  where  in  which  it  now 
is,  we  would  most  likely  conclude  the  second  one  to  be  it.  Respecting  simi- 
lar truths  grounded  in  the  ego,  therefore,  the  heleration  of  their  times  alone 
destroys  the  identity:  respecting  similar  truths  grounded  in  the  non-ego, 
time  being  the  same,  the  heleration  of  their  wheres  destroys  the  identity! 
The  power  of  the  mind  to  heterate  depends  upon  the  time  and  space. 

And  now  we  look  at  John  and  receive  a  mental  effect,  and  again  look 
at  him  and  receive  a  similar  effect,  the  times  of  these  effects  can  be  heterated, 
and  hence  there  are  two  similar  existences  grounded  in  the  ego,  wliich  can 

.  be  compared  siith  each  other.  But  if  we  project  these  existences  and  ground 
Ihera  in  the  non-ego,  at  the  very  time  we  last  looked  at  John,  we  knew^f  but 
one  where  for  these  two  subjective  existences  to  exist  objectively,  and  hence 
no  heleration,  objectively,  of  their  wheres  can  be  made;  and,  therefore,  as 
they  are  subjectively  similia,  they  are  objectively  to  us  homon:  and  henco 
we  can  say  that  John  is  John,  or  that  John  is  himself.  The  mind  can  pIso 
gain  a  truth  grounded  in  the  non-ego'and   afterwards  recall  it  by  what  w^e 

•call  memory:  and  as  often  as  the  mind  does  thus  recall  one  and  the   same 
4  objective  truth,  so  many  subjective  truths  inter  se  similia,  but  not  identical, 

will  pass  through  the  ego,  any  two  of  which  may  be  compared  and  projected! 
And  respecting  the  projection  of  truths  from  the  ground  of  the  ego  into  that 
ot  the  non-ego,  we  have  already  seen  heretofore,  how  existences  are  divided 
by  the  mind  into  those  grounded  in  the  ego  and  those  grounded  in  the  non- 
ego. 

And  hence  the  meaning  cf  the  proposition  "John  is  himself,"  is  tTiat 
John,  grounded  in  the  non-ego,  and  iiimseij.-,  grounded  in  the  non-ego  are 
the  same  thing;  John  and  John  who  are  subjectively  hetera  are  objectively 
homon.    We  may  say  that  John  and  himself  are  the  same  thing,  or  that  John 

.  and  himself  exist  identically,  or  that  John  exists  as  himself:  whatever  itay 
be  the  words  and  their  syntactical  relations,  the  two  subjective  existences, 
each  of  which  we  call  John,  are  objectively  the  same,  and  what  is  affirmed 
by  the  proposition,  is  homon.    None  of  these  expressions,  however,  mark  in 

^  words  with  enlire  fullness  the  whole  of  the  mmd's  operations,  but  merely 
state  or  set  down  the  existences  compared  and  affirm  the  result  of  the  com- 
parison. And  in  a  large  class,  of  propositions,  all  of  that  class,  which  w'e 
have  called  homonical,  the  result  of  the  comparison  made  by  the  mmd  is 
homon,  homon  is  the  thing  affirmed.  This  is  always  the  case  in  those  propo- 
sitions which  defined  words,  i.  e.,  in  which  the  meaning  of  a  word  is  ex- 
plained by  some  syuonkn  or  equivalent  expression:  as  taithfulibss  is  fidelity. 


55 
i.  e.,  the  meaning  of  the  word  faithfulness  and  that  of  fidelity  are  homon 
The  following  propositions  are  similar  to  the  one  first  spoken  of:  "Sun  is  the 
name  of  the  orb  of  day;"  "Death  is  the  name  ot  the  etid  of  life;"  "Term  is 
a  name  given  to  each  df  the  names  which  distinguish  the  existences  com- 
pared in  a  proposition;"  and  so  on.  All  of  these  propositions  are  homoni- 
cal, homon  is  affirmed  in  each  one  of  them. 

Such  propositions  as  the  one  above  have  been  called  verbal,  because  the 
existences  compared  in  them  are  words.  And  according  to  the  old  but  erro- 
neous system  of  predication,  in  such  propositions,  one  name  is  predicated  or 
affirmed  of  another.  One  name,  however,  can  not  be  affirmed  of  another, 
uof  canone  existence  be  affirmed  of  another;  the  only  thing  that  can  be 
affirmed,  in  such  propositions  as  we  are  now  treating  of,  is  homon.  In  those 
propositions,  also,  which  arc  called  real,  in  these,  which  explain  the  nature  of 
the  thing  defined,  homon  is  the  thing  affirmed;  as  "A  triangle  (the  thing 
signified  by  the  word)  is  a  figure  having  three  sides  and  three^angles,"  "Ihe 
eye  is  ^  physical  organ  by  which  we  see,"  "A  primary  property  of  matter  is 
impenetrability,"  and  so  oo, 

•  But  in  the  proposition  "John  is  John,"  which  we  considered  a  little 
while  ago,  we  notice  that  both  the  subject  and  predicate  are  aggregate  exis- 
tences, and  that  each  one  is  compared  with  the  other  in  the  aggregate  as  a 
totality.  Now  when  the  subject  is  an  aggregate  existence,  and  U^is  viewed  as 
atotality,  andiillof  itsgregaria  are  taken  collectively,  the  predicate  must 
also  be  compared  in  the  aggregate  in  all  homonical  propositions:  for  an 
aggregate  existence,  as  a  totafity,  can  not  be  the  same  as  a  simple  existence, 
a  gregarium,  and  vice  versa.  But  there  are  homonical  propositions  in  whicli 
the  subject,  in  appearance,  would  seem  to  be  an  aggregate  existence  viewed 
as  a  totality,  while  the  predicate  is  very  plainly  a  simple  existence,  a  gre- 
garium :  we  must  therefore  examine  such  propositions. 

AVe  must  always  keep  in  view  that  in  every  simple  proposition,  two 
existences  and  only  two  are  compared:  in  logical  propositions  these  two  ex- 
istences are  immediately,,compared,  and  in  conclusional  propositions  they 
are  mediately  compared.  These  two  existences  may  be,  each  of  them,  sim- 
ple, aggregate,  or  collective;  yet  there  can  but  two  enter  into  the  comparison 
in  the  proposition  of  which  the  result  is  expressed  in  words.  And  one  of  the 
difflculUes  in  the  way  of  understanding  propositions,  is  to  ascertain  what  are 
really  the  two  existences  and  the  nature  of  each  of  them  in  the  proposition.  , 
This  difficulty  has  not  been  overcome  by  any  writer  upon  logic,  heretofore, 
with  whose  work  we  are  acquainted. 

Now  when  we  say  that  Snow  is  white,  or.  that  Iron  is  fusible,  we 
might  believe  that  snow  and  iron,  aggregate  existences,  are  compared  in'  to- 
tality, with  their  predicates  respectively:  this  ho-wever,  would  be  entirely 
erroneous.    And  in  order  to  ascertain  and  clearly  exhibit  by  the  wording  of 


56 
t]i£  proposition,  tlie  two  things  wliich  are  really  compared,  we  have  to   stale 
the  proposition  thus;  One  of    the  capacial  gregaria  of   iron  is  fusibility,  a 
proposition  in  whiclf  a  like  result  is  obtained  as  in  the  other,  and   in  which 
two  simple  existences,  which  arc  the  things  really  compared  distinctly  appear. 
And  if  the  .proposition  be  stated  so  that  the  horaonical  nature  of  it  also  shall 
clearly  appear,  it  will  read  thus;  One  of   the  capacial   gregaria  of    iron  and 
lusibility  are  homoH.    And  in  ail  homonical  propositions  in  which  the  sub- 
ject is  an  agffregate  existance  and  the  predicate  a  simple  one,  it  is  only  one  of 
the  greuariaof  the  aggregate  existence,  that  is  compared.     In  the  proposi- 
tion,   ditaline    was    ambitious,   wiicn  the    things  actually   compared    are 
clearly  set  out  it  will  read  Ono  of  the  capacial  gregai'ia  of  Cataline  was  am- 
bition,  i.  e.,  one  of   the  capacial  gregaria  of   Catalin«r  and   ambition  are 
homou.    Wlien  we  say  Red   is  red,  the  result  of    the  comparison  is  easily 
seen,  because  we  plainly  see  that  both  subject  and  predicate  are  simple  exis- 
tences; but  when  the  real  subject  is  covered  up  by  a  term  which  signifies  an 
aggregate  existence,  and  the  predicate  is  simple,  we  are  misled. 

And  hence  in  such  propositions  as  Ironjs  fusible,  writers  have  said 
that  the  predicate  is  affirmed  of  the  subject,  or  that  the  predicate  iscpntmned 
in  the  subject  and  so  on,  all  of  which  expressions  not  only  give  erroneous 
notions  of  the  nature  of  propositions  in  general,  but  per  se  they  are  utterly 
false:  for  the  existence  which  propositionally  is  called  the  predicate  is  com- 
pared with  the  subject  and  the  result  of  such  comparison  is'what  is   atlirmed 
in  every  proposition.    And  although  fusibility  is  one  of  the  capacial  gregaria 
of  iron,  and  it  is  contained  in  this  aggregate  txistence,yet  this  aggregate  ex- 
istence in  totality  is  not 'the  subject  of  the  proposition  -Iron  is  fusible,  but 
this  capacial  gregarium  of  iron  is  the  subject.    We  have  already  shown  that 
in  every  proposition   two  subjective  existences,  i.  e.,  existences  grounded   in 
in  the  ego  are  compared:  and  in  the  proposition  Iron  Is  fusible,  twx)  fusi- 
bilities are  sujectively  compared,  and  subjectively  they  are  similia:  and  then 
they  are  objectively  located  as  homon  in  the  aggregate  existence  iron,  and 
this  is  the  result  of  the  comparison  in  the  proposition  Iron  is  fusible. 

Now  as  there  are  but  two  classes  of  subjects,  simple  and  aggregate, 
and  so  also  of  predicates,  it  would  not  be  necessary  at  present  to  say  any- 
thing further  respecting  homonical  propositions  were  there  not  sometimes 
set  down  the  words  all,  evtry,  most,  some,  the  whole  of,  none,^oth,  etc., 
alonir  with  subjects  and  predicates:  but  homonical  propositions  in  which 
these  words  are  either  expressed  or  understood  need  a  further  investigation. 
And  when  we  say  that  All  iron  is  fusible,  which  writers  have  called  a  uni- 
versal proposition,  what  do  we  mean  by  the  words  All  kon  ?  As  iron  is 
an  aggregate  existence,  let  us  first  examine  a  simpler  case;  take  the  proposi- 
tion All  red  is  red,*  i.  e..  red  and  red  are  homon.  Now  almost  any  one  will 
say  that  this  proposition  is  self-evident,  because  were  the  predi6atc  anything 


57 

else  than  red,  it  could  not  objectively  be  the  same  thing  as  the  subjept,  which 
is  red.  'Now  this  explainalion  can*easily  b6  applied  to  unravel  the  mysteries 
of  the  proposition  All  iron  is  fusible.  For  this  proposition  may  be  thus 
stated,  Oneof  the  capacial  gregarium  of  all  iron  and  fusibility  are  homon. 
And  from  this  proposition,  it  must  appear,  that  were  fusibility  lacking  in  an 
aggregate  existence,  that  existence  could  not  be  ipon.  Fusibility  is  a  neces- 
sary gregarium  in  any  aggregate  existence,  which  we  distinguish  by  the 
name,  iron;  and  consequently  it  must  exist  in  this  piece,  that  piece,  and  in 
all  pieces  of  similar  aggregations. 

The  word  all  standing  before  iron  does  not  indicate  that  the  mind 
must  have  made  what  is  usually  called  an  induction,  i.  e.,  that  the  mind  from 
a  great  number  of  l^tances  has  determined  the  laws  of  nature  to  be  uniform, 
and  therefore  this  piece  and  that  piece  will  fuse.  The  discovery  of  the  capa- 
cial gregarium,  fusibility,  in  one  single  piece  of  iron,  if  by  this  gregarium 
we  distinguish  an  aggregate  existence  from'  others,  and  mark  the  distinction 
by  the  w>rd  iron,  will  enable  us  to  say  with  certainty  and^ruth  that  All  iron 
is  fusible;  for  in  doing  so,  we  merely  state  that  one  of  the  necessaiy  gre- 
garia of  an  aggregate  existence,  which  we  distinguish  by  the  name  iron,  and 
fusibility  are  homon.  .  That  there  may  be  other  gregar/a  in  the, aggregation, 
of  which  as  yet  we  know  nothing,  does  not  change  the  case  at  all. 

Suppose  a  person  to  be  taken  into  a  large  room  in  which  there  were 
four  kinds  of  balls  upon  different  shelves  around  the  apartment,  and  he  be 
required  to  give  distinguishing  names,  which  would  enable  him  to  speak 
afterwards  about  the  bulls,  respecting  merely  their  tastes  and  colors.  lie 
would  take  up  the  first  one  at  hand,  and  perceive  that  it  was  of  a  red  color 
and  had  a  sweet  taste,  and  therefore  he  would  name  this  ball  A.  Thpn  every 
ball  in  the  room  that  was  red  and  sweet,  as  balls  of  color»  and  tastes,  which 
are  inter  se  similia,. can  not  be  diflerentiated,  must  be  called  A  from  a  men- 
tal necessity.  And  by  the  name  A,  they  are  afterwards  distinguished  from 
those  that  are  blue  and  sour,  which  might  be  called  B,  and  from  those  which 
are  while  and  bitter,  which  might  be  called  C,  and-  so  on.  But  so  soon  as  he 
had  given  the  name  A  to  distinguish  the  first  ball  of  a  red  color  and  ss^'eet 
taste  from  others,  all  balls  of  a  red  color  and  sweet  taste  must  be  called  A, 
and  if  so,  could  he  not  immediately  afier  naming  the  first  ball, 
have  said  with  perfect  certainty  and  truth  that  all  A  is  red  and  all  A  is  sweet? 
And  it  afterwards,  a  red  ball  should  be  found  that  was  sour,  it  would  not  be 
an  A,  but  it  must  be  called  by  some  other  name. 

But  an  Indian,  before  the  discovery  of  America,  might  have  said  that 
all  men  are  red,  for  he  had  never  seen  any  man  of  a  different  color,  yet  his 
assertion  would  not  have  been  truQ.  The  ancients  also,  might  have  said  and 
did  say,  that  all  swans  are  white,  yet  such  is  not  the  case.  And  the  error  in 
both  these  ca^es  lies  in  taking  the  gregarium  of  a  particular  object  or  objects 


and  making  this  gregarium  in  our  mind,  one  of  the  necessary  gregaria  to  dis- 
tinguish this  object  from  others,  when  ^t  is  not  so:  there  were  other  things 
red  besides  Indians,  and  other  things  white  besides  swan's,  when  animals 
were  distinguished  by  names:  the  color  was  not  one  of  the  gregaria  by 
which  these  objects  were  necessarily  distinguished. 

But  we  have  said  that  aggregate  existences  are  distinguished  inter  se 
by  the  facial  and  capacial  gregaria  co-existing.  And  hence  did  one  aggre^ 
gate  existence  contain  similar  facial  but  not  similar  capacial  gregaria  with 
another,  the  two  aggregations  would  not  be  similia,  and  they  could  not  be  in- 
telligently distinguished  by  the  same  name.  A  distinguishing  name  is  r. 
word  taken  at  pleasure  to  distinguish  existences  inter  se;  and  when  It  sUnds 
for  an  aggregation,  any  one  of  the  gregaria  Bine  qua*)n,  can  not  bo  lacking, 
and  the  aggregation  be  called  by  the  same  name  as  an  object  in  which  it 
exists.  Charcoal  and  the  dinmond  are  said  to  be,  as  elements,  similia,  yet  the 
gregaria  differ  and  consequently  we  can  not  speak  of  each  intelligently  and 

use  the  same  name.  • 

But  how  then,  say  you,  is  it  that  %  black  swan  and  a  white  one  may 
both  be  called  swans ?  Simply  because  they  are  differentiated  into^ swan's 
irrespective  of  their  colors,  just  as  red  and  white,  as  we  have  seen,  are  first 
diffeientiated  into  color,  amd  then  distinguished  inter  se,  by  the  names  red 
and  white.  All  men  are  mortal,  is  a  proposition  of  the  same  kind  as  All  iron 
Is  fusible.  Mortality  is  one  of  the  capacial  gregaria  sine  qua  non  of  man, 
and  a  living  being  not  subject  to  death  would  not  be  a  man.  Ihe  proposi- 
tion All  m'en  are  mortal,  however  is  a  very  different  one  from.  All  men  are 
mortals-  the  first  affirms  homon  of  mortality  and  one  of  the  cappcial  gre- 
garia sine  qua  non  of  man;  the  second  affirms  man  and  one  of  the  aggregate 
existences  called  mortals  to  be  homon.  AH  men  are  animals,  and.  All  sheep 
are  animals,  are  similar  propositions, and  they  may  be. thus  interpreted:  man 
and  one  species  of  animals  are  homon,  sheep  and  one  species  of  animals  are 

homon.  '  .  .  .        .., 

But  to  pursue  further  the  effect  of  the  word  all  in  propositions,  if 
when  man  was  first, placed  upon  the  earth,  he  had  lived  to  the  age  of  tcn| 
thousand  years  without  a  death  occurring,  and  if  during  that  period  he  had 
invented  language  and  distinguished  himself  by  the  name  man,  it  is  plain 
that  mortality  would  not  have  been  in  his  mind  one  of  the  capacial  gre- 
garia of  himself:  he  would  not  at  least  have  known  this  by  direct  observa- 
tion    And  if  during  this  time,  no  constituttonal  changes  among  external 
objects  had  come  to  his  knowledge,  it  is  evident  that  he  would  have  known  1 
nothing  at  all  about  the  capacial  gregaria  of  objects;   but  all  the  names  inl 
his  language  would  have  been  signs  to. distinguish  simple  existences  inter  se, 
and  aggregations  of  facial  gregaria.    And  therefore  all  the  aggregate  exis- 
tences now  classified  by  their  capacial  gregaria  and  marked  by  distinguish- 


i  69 

• 

ing  names,  would  have  remained  unclassified.    And  then  each  one  of  the 
facial  gregaria,  whic^^was  a  sine  qua  non  of  any  class,  would  have  been  a 
necessity  in  order  that  any  object  might  have  been  called  by  the  name  given 
to  individuals  of  the  class.    Names,  of  course,  under  the  circumstances 
would  have  been  few  in  Bumber.    But  suppose  now,  that  at  the  end  of  the 
period  above  spoken  of,  one  of  the  human  species  had  died,  here  would  have 
been  to  mankind  a  new  truth  learned  by  observation.    And  were  this  instance 
of  deatU  then  made  known  to  all  the  living,  all  subsequent  deaths  would  not 
have  been  new  truths,  but  other  instances  of  similar  truths.    And  although 
non  simile  est  idem  or  non  similia  sunt  idem,  objectively,  yet  subjectively 
similia  are  the  same  thing  if  time  be*  left  out  of  tho  question.    And  hence 
respecting  the  knonrlcdge  of  truths  in  the  mind,  the  recurrence  of  similia  are 
regarded  and  often  spoken  of   as  other   instances  of  the  same  truth,  Although 
they  ar^not  homon  i)ut  similia;  their  times  arehetera  and  therefore  the  truths 
are  similia,  but  were  their  times  homon,  the  truths  also,  would  be  subjectively 
homo%    Now  if  we  have  gained  the  knowledge  of  one  individual  of  similia, 
we  have  gainod  all  the  knowledge  we  will  ever  have  of  tho  similia,  except- 
ing their  number  or  instances.    And  therefore  after  pnc  death  had  occurred, 
the  question  would  have  been,  men  being  similia  in  those  gregaria  which  to- 
gether make  the  object  distinguished  by  the  name  man,  is  death  one  of  these 
capacial  gregari^    That  it  is  could  have  been  proved  to  men  under  the 
above  circumstances  only  by  a  process  of  reasoning  which  we  shall  develop 
hereafter.    (See  book  1,  chapt.  xxii.)    But  so  soon  as  it  is  established  to  be 
such,  it  is  a  sine  qua  non  of  man  and  hence  we  say  that  death  and  one  of  the 
capacial  gregaria  of   all  men  are  homon.    And  as  aggregate  existences  are 
composed  of  certain  facial  and  capacial  gregaria,  which  are  the  very  things 
which  distinguish  them  into  classes  of  similia,  when  any  oi^e  of  these  gre- 
garia sine  qua  non  is  known  and  given  a  name,  it  may  be  made  the  predicate 
of  an  homonical  proposition,  in  which  the  word  all  names  the  sum  totum  of 
the   aggregate  existences  for  any  one  of  which  the  noun  placed  after  all 
.  stands  as  the  name.    And  hence  that  all  iron  is  fusible,  when  fusibility  is  once 
in  our  minds  a  sine  qua  non  of  iron,  is  a  necessity  of  our  miyds.  It  may  TJe  said 
that  fusibility  is  not  a  gregarium  sine  qua  non  to  distinguish  iron  from  other 
things;  for  gold  and  other  metals  possess  it.    This  is  true;   but  go  one  step 
back  into  the  class  of  things  called  by  the  narne  metal,  and  we  will  find  fusi- 
bility to  be  one  of  the  distinguishing  gregaria,  and  in  subclassifications  this 
.  gregarium  must  pass  int^  each  of  the  subclasses;- for  they,  each  of  them, 
under  the  name  metal  possessed  It.    And  hencei  by  adding  the  words  all 
and  EVERY  to  the  name  of  an  aggregate  existence  and  then  making  the  term 
the  subjective  one  of   an  homonical  proposition  with  a  simple  existence  as 
the  predicate,  we  show  this  simple  existence  named  in  the  pr^icate  to  be  one 
of  the  gregaria  sine  qua  non  of  the  aggregate  existence  named  in  the  subject. 


eo 

All  gold  is  proof  against  the  effect  of  nitric  acid,  i.  e.,  one  of  the  capacial 
gregaria  sine  qua  non  of  g»ld,  and  proof  against  tlA^ffect  of  nitric  acid  are 
homon. 

But  we  must  now  examine  the  function  of  the  word  some  when  placed 
before  the  name  of  an  aggregate  existence  in  a  proposition.  Take  the  propo- 
sition Some  ink  is  red,  i.  e.,  one  of  the  facial  gregaria  of  some  ink  and  red 
arehomon.  Now  it  must  appear  that  the  facial  gregarium  here  mentioned  is 
not  a  sine  qua  non  of  ink,  but  that  it  is  one  which  compared  witli,  some  other 
color,  enables  us  to  differentiate  inks.  Some  therefore,  as  it  names  the^part 
of  a  whole,  shows  also  by  being  pjaced  before  an  aggregate  existence  in 
homonical  propositions,  that  the  gregarium,  which  appears  as  a  simple  exis- 
tence in  the  predicate,  is  not  a  sine  qua  non  of  the  clHIs  of  aggregate  exis- 
tences distinguished  by  the  name  which  appears  in  the  subje'ct  and  named 
by  the  noun  after  some.  *         •  '  *  * 

We  do  not  deem  it  pecessary  to  pursue  the  subject  of  homonical 
propositions  further  at  present.  If  the  reader  will  carefully  stud>  what  has 
been  said  already,  we  think  he  will  be  a^le  to  follow  an*  understand  the 
arguments,  which  we  will  -advance  hereafter.  We  will,  however,  set  down 
several  homonical  propositions  in  the  language  that  is  used  in  common  dis- 
course, and  the  reader  can  change  the  phraseology,  so  aa  to  make  the  result 
aflSrmed  appear  plainly  to  be  homon:  Some  men  are  black-eyed;  All  fowls 
lay  eggs ;  All  gold  is  maleable ;  God  is  love ;  An  apple  is  an  apple ;  A  straight 
line  is  the  shortest  distence  between  two  points  in  space;  Ice  is  frozen  water; 
Schuylkill  is  the  name  of  a  river  in  Pennsylvania;  Washington  died  at 
Mount  Vernon ;  We  are  living  in  the  nineteenth  century  of  the  Christian  era; 
Columbus  discovered  America  A.  D.  1492:  Shakespeare  was  a  dramatic 
author;  Sophocles  wrot^  ^dcpus  Tyrannus;  Newton  discovered  the  univer- 
sal law  of  gravitation. 

CHAPTER  XI. 

-    ^  HETERICAL  PROPOSITIONS. 

Having  Seated  of  homonical  propositions,  we  hope,  with  partial  suc- 
cess, we,come  now  to  speak  of  the  second  class,  which  we  hare  called  heter- 
cal  propositions.  And  heterical  propositions  affirm  results,  which  are 
directly  the  opposite  of  those  affirmed  by  homonical  ones,  and  consequently 
the  twa  classes  £\re  differentia;  and  when  a  proposition  of  the  one  class  is 
spoken  with  reference  to  the  other,  it  denies  the  affirmation  made  by  the 
other.  If  any  person  affirm  that  A  is  B,  i.  e.,  Ihat  A  and  B  are  homon,  and 
another  person  reply  that  A  is  not  B,  i.e.,  that  A  and  be  are  hetera,  the  latter 
makes  and  aflSrmation  contradictory  of  the  affirmation  of  the  former  and 
vice  versa.  " 

Now  if  we  take  two  twenty  dollar  gold  pieces  which  are  inter  se 


61 

jsimilia,  and  lay  them  before  us,  any  person  will  say  this  piece  is  not  that  one. 
But  the  two  pieces  being  inter  se  similia,  if  you  hand  one  of  them  to  a  per- 
json,  and  then  take  it  again  and  put  the  two  together,  and  ask  the  person  which 
one  lie  had  in  his  hand,  he  can  not  tell.    How  then  does  any  one  know   that 
this  piece  is  not  that  one,  i.  e.,  that  the  two  pieces  are  not  homon,  but  hetera? 
Simply  because  the  wheres  of  the  two  pieces  at  the  same  time  can  be  heterated. 
But  is  not  th«  proposition.  This  piece  is  not  that  one,  an  independent  propo- 
sition, i.  e.,  a  proposition  expressed  without  reference  to  any  other?    If  it  is 
such,  tlien   it  can  not  contain  a  denial  or  negation  of  the  subject,  as   it   is 
generally  supposed,  but  it  positively  affirms  this  piece  and  that  piece  to  be 
hetera.    You  can  not  numerically  count  pieces  of  money  without  hcterating 
them,  and  you  can  not  express  in  words  the  heteration  of  them  without  using 
an  heterical  yroposition  or  propositions.    What  is  the  difference  between 
These  two  pieces  are  separate  existences,  and  This  piece  is  not  that  one;  leav- 
ing the  wording  out  of  the  consideration  ?    The  difference  is  this,  the  former 
propositien  never  could  have  been  put  into  words  at  all,  without  the  latter 
one  having  first  been  menially  at  least  eiuntiated:  the  latter  proposition 
must  preceed  the  former  in  the  mind,  or  a  knowledge  of  the  former  never 
could  be  gained:  in  eflect,  however,  the  two  are  alike.    The  former  proposi- 
tion may  be  resolved  into  This  piece  is  an  existence  and  that  piece  is  an  exis- 
tence and  the  whole  expression  is  exquivalent  to  This  piece  is  not  that  piece 
1.  e.,  thi8  piece  and  thatpiece  are  hetera.    And  every  heterical  proposition  may,' 
in  effect,  be  exactly  expressed  by  the  use  of  two  homonical  ones,  by  placin<^ 
the  distinguishing  names  of  hetera,  this  and  that,  befcre  their  subjects:  two 
homonical  propositions  may  also  be  condensed  into  one  similical   or  com- 
mensural  one;  or  they  may  be  differentiated  or  incommensurated,  in. differ- 
ential or  incommensural  propositions,  as  we  shall  see  hereafter.     But  there 
must  be  an  heteration  of  existences  in  the  mind  before  any  proposition  wlwt- 
ever  can  be  expressed;  for  we  have  already  shown  that  the  process  of  heter- 
ation lies  at  the  very  foundation  of  knowledge.     And  this  process  of  hetera- 
tien  can  not  be  a  negative  process;  it  must  be  positive  or  it  would  amount  to 
nothing,  and  its  positive  character  can  not  be  expressed  but  by  an  affirma- 
tion.   This  has  been  overlooked,  heretofore,  by  all   writers  upon  logic.    Be- 
cause the  panicle  not  is  found  in  the  proposition,  it   has   been   universally 
believed  that  the  predicate  denied  something  of  the  subject,  or  that  the  predi- 
cate was  denied  of    the  subject;  a   proposition,  which  follows   legitimately 
enough  from  an  other,  which  is  that  when  this  particle  is  omitted,  something 
is  affirmed  of  the  subject,  but  both  of  these  suppositions  are  untrue.    The 
predicate  is  no  more  affirmed  or  denied  of  the  subject  in,  propositions  than 
the  subject  is  of  the  predicate;   the  two  existences  are  compared,  the  one 
with  the  other,  and  that  which  is  affirmed,  in  all  cases,  is  the  result  of  the 
comparison.    It  is   impossible  for  the  human  mind  to  affirm  or  deny  one 


62 
cxistancc  of  another ;    all  that  we  can  do  is  to  affirm  some  relation  existing 

between  existences. 

One  and  the  same  existence  of  the  non-ego  can  not  sustain  heterical, 
similical  or  differential  relation  to  the  ego  in  an  homonical  time;  for  it  it 
could,  we  could  have  no  knowledge  of  identity.  When  we  lay,  thereiore, 
that  A  is  not  B,  we  do  not  mean  that  A  does  not  exist,  or  that  B  does  not 
exist,  for  both  must  have  an  existence  .grounded  in  the  ego  at  least,  or  we 
could  not  put  their  separate  names  down  on  paper;  but,  by  A  is  not  D,  we 
mean  that  A  and  B  exist  heterically,  that  A  and  B  are  hetera.  The  particle, 
NOT,  therefore,  in  propositions,  stands  as  the  sign  of  hetcrution  made  by  the 
mind,  but  the  result  of  the  heteration  is  positive,  and  it  is  affirmed  in  all 
propositions  containing  this  particle.  And  we  lay  down  this  rule:  That 
whenever  the  wheres  ot  existences  grounded  in  the  non-ego  can  be  heteraled 
in  an  homonical  time,  and  whenever  the  times  of  existences  grounded  in  the 
e^o  can  be  heterated,  the  heterical  relations  of  these  existences  are  expressed 
in  heterical  propositions. 

In  homonical  propositions  we  saw  that  the  wheres  of  the  two  existences 
compared,  could  not  at  the  same  time  be  heterated.  When  we  say,  John  is 
John,  the  subject  and  predicate  subjectively  have  the  same  where,  but  not  an 
homonical  time:  John  and  John  objectively  have  the  same  whereat  the  same 
time,  and  therefore,  objectively  they  are  homon.  But  the  objective  John  and 
the  subjective  John  are  hetera  because  their  wheres  at  the  same  time  can  be 
heterated;  and  John  and  John  are  subjectively  hetera  because,  though,  their 
wheres  are  homon,  they  can  not  have  an  homonical  time.  And,  thercfforo, 
homonical  and  heterical  propositions  contradict  each  other,  when  their  sub- 
jects arc  similia  in  every  respect,  and  their  predicates  similia  leaving  the 
particle  not  out  of  the  consideration. 

•  Now  in  heterical  propositions,  we  make  no  account  of  the  similarity 
or  dissimilarity  of  existences;  all  we  care  about,  is  to  be  able  to  heterate  the 
wheres  of  existences  grounded  in  the  non-ego  at  any  given  time,  and  the 
times  of  existences  grounded  in  the  ego,  and  then  we  affirm  hetera.  And 
hence  if  we  place  two  white  marbles  before  us,  the  color  of  the  one  and  that 
of  the  other  being  perfectly  similia.  yet  we  say  that  the  color  of  the  one  is  not 
that  of  the  other,  i.  e.,  the  color  of  the  one  and  that  of  the  other  are  hetera; 
for  the  wheres  of  these  colors  can  be  heteraled.  When,  however,  we  look  at 
A  (one)  marble  and  say  The  color  of  this  marble  is  white,  or  to  use  the  short 
expression.  This  marble  is  white;  the  color  of  the  marble  and  wiiitp:  sub- 
jectively have  the  same  where,  but  heterical  times;  but  when  we  project  these 
subjectively  heterical  colors  which  are  inter  se  similia,  into  (he  objective 
marble,  they  both  have  the  same  where  at  the  same  time  and   therefore,  we 

affirm  homon. 

Now   we  have,  heretofore,  divided  subjects  and   predicates   into   two 


62 
classes,  simple  and  aggregate.    And  of  simple  cjistences,  some  become  the 
gregaria  of  aggregations,  others  do  not.    Time  and  space  are  never  gregaria. 
And  we  must  have  observed  that  it  is  the  relations  of  simple  existences  or  of 
aggregations  in   time  and   space,  that  enable  us   to   affirm  homon  or  hetera; 
the  power  of  the  mind  to  heterate  depends  upon  time  and  space.    When  we 
say  tbat  this  apple  is  not  that  one,  we  apparently  compare  one  apple  with  the 
other  immediately:  the   existences,  however,  which   are   immediately  com- 
pared, are  the  wlieres  of  the  one  and  the  other  at  the  same  time.    But  when 
we  say  subjectively,  An  onion  is  not  a  peach,  this  proposition  is   more   than 
heterical   and   it  belongs  to  the   differential   class,  which  we  will  treat  of 
hereafter.    If,  however,  we  say  this  peach  is  not  that  onion,  we  heterate   the 
wheres  and   affirm  hetera,  and   tliis  is  shown   by  the  words   this  and  that 
And  if  the  reader  will  bear  in  mind,  that  whenever  he  can  heterate  the  wheres* 
of  existences  at  the  same  time,  or  sulyectivelj  heterate 'the  times  of   subjec- 
ive  existences,  the  proposition  may  be  iieterical,  we   think  he  will    be  able  to 
detect  heterical  propositions,  whenever  he  may  find  them  in  books  or  couver 
sation,  by  some  words  which  distinguish  hetera. 

We  will  set  down  a  few  heterical  propositions  for  practice:  Philadel- 
phia is  not  New  York;  The  Pacific  Ocean  is  not  the  Atlantic;  My  hat  does 
not  lie  on  the  floor;  The  birth-place  of  Washington  was  not  Boston;  This 
hand  is  not  that  one. 

CHAPTER  XII. 

8TMILICAL  PKOPOSITIOXS. 

When  treating  of  homonical  propositions,  we  shawed  that  absolute 
identity  makes  no  part  of  our  knowledge;  that  in  all  homonical  proppsitions» 
the  exisU^nces  compared  are  always  subjectively  hetera;  that  heterical  results 
in  the  order  of  time  always  precede  our  knowledge  of  identity,  an«i  are  the  v 
very  first  results  obtained  ;  that  the  knowledge  of  the  existence  of  any  simple 
existence  is  dependent  upon  hetera;  and  that  unless  heterical  results  can  be 
obtained,  chaos  reigns  supreme.  If  I  see  a  horse  to-day  and  to-morrow  see 
the  same  horse  again,  nevertheless,  subjectivel}',  I  have  seen  two  distinct 
horses;  and  when  viewed  as  existences  grounded  iu  the  ego,  I  distinguish 
them  by  heleraling  their  times,  but  when  projected  onto  the  ground  of  the 
non-ego,  the  heteration  of  their  times  does  not  distinguish  them  and  as  I  can 
not  heterate  their  wheres  at  the  same  time,  I  caji  not  distinguish  them  at  all, 
but  pronounce  them  to  be  homon. 

But  suppose  that  sulgeclively  I  consider  heterical  existences  and  can 
not  further  discriminate  them,  and  objectively  also  I  heterate  the  existences 
but  can  distinguish  them  no  further,  then  we  call  the  existences  similia.  And 
Jience  when  we  can  heterate  subjective  existences,  but  can  proceed  no  further, 
tlic  existences  are  subjectively  similia,  and  when  we  can   heterate  objective 


64 

existences  but  can  distinguUh  themno  further,  tbe^xistences  are  objectively 
similla.  And,  therefore,  objective  bomon  is  always  subjective  similia,  but 
not  always  vice  versa;  for  subjective  similia  may  also  be  objective  similia. 
Subjective  homon  can  not  be  expressed  in  a  proposition,  i.  e.,  two  acts,  feel- 
ings or  states  of  mind  can  not  be  one  and  the  same,  they  must  be  beiera,  and 
one  thing  per  se  can  not  be  compared. 

Take  the  proposition  This  orange  tastes  like  that  one,  i.  c.,  the  tastes 
of  this  one  and  of  that  one  are  similia.  Now  the  sensations  of  the  taste  of 
the  one  and  of  the  other,  as  existences  grounded  in  the  ego,  arc  similia,  and 
when  projected  onto  the  ground  of  the  non-ego,  each  one  is  a  gregarium  of 
heterical  objects  whose  wheres  can  be  heterated,  and  therefore,  objectively.the 
tastes  are  similia.  We  need  not  proceed  further  at  present  with  similical 
propositions.  We  will  subjoin  a  few  examples  for  practice:  This  apple 
tastes  like  that  one;  John  is  like  his  father;  Time  is  like  a  silent  river. 

CHAPTER  XIII. 

DIFFERENTIAL  PROPOSITIOJTS. 

We  proceed  now  to  the  consideration  of  the  fourth  class  ef  proposi- 
tions, namely,  differential  propositions.  And  when  two  subjective  existences 
can  be  discriminated  by  anything  besides  their  times,  the  existences  are  sub- 
jectively differentia.  The  effect  produced  upon  and  within  the  mind  by  red 
is  different  in  kind  from  the  effect  produced  by  green,  and  hence  the  two 
effects  are  not  only  hetera  subjectively,  but  also  differentia.  And  existences, 
which  are  subjectively  differentia,  must  necessarily,  if  each  have  a  corres- 
ponding objective  ^istence,  be  also  objectively  differentia.  But  ho#  or  why 
it  is  that  the  mind  is  able  to  discriminate  between  red  and  green,subjectively, 
we  do  not  sufficiently  understand.  The  two  objects,  which  produce  severally 
these  different  effects  upon  our  minds.  Sustain  in  some  manner  different  re- 
lation to  the  ego:  they  are  other  different  elemeitary  principles,  or  the  one 
is  composed  of  more  or  differently  arranged  gregaria  than  the  other.  Let 
this  be  as  it  may,  for  logical  purposes  it  makes  no  differtncc  to  us;  every 
person  will  distinguish  subjectively  and  objectively  red  from  green,  and 
consider  them  to  be  things  differing  in  kind — differentia. 

We  have  already  stated  that  subjects  and  predicates  of  propositions 
are  either  simple  or  aggregate  existences.  And  when  both  subject  and  predi- 
cate are  simple  existences,  the  differentiation  clearly  appears.  That  red  is 
not  green ;  will  easily  be  seen  to  be  a  differential  proposition.  The  iign  not 
does  not  indeed  of  itself  indicate  whether  the  existences  have  been  differen-* 
tiated  or  meiely  heterated.  But  hcteration  can  easily  be  distinguished  from 
differentiation,  if  we  look  at  the  terms  of  the  proposition.  In  the  heterical 
proposition,  This  red  is  not  that  green ;  we  see  that  the  terms  are  particular 
names,  the  names  of  individual  existences,  and  that  the  distinguishing  heteri- 


65 
hetericiil  names,  this  and  that  are  joined  wiih  the  common  names,  red  an  I 
GRKEN,  and  thus  making  red  and  green  the  names  of  particular  inlividuaN: 
Wliile  in  tiie  differential  i)r<>poftilion  Ued  is  not  green,  red  and  green  are 
unlimited  common  names.  Tlie  name  red  stands  for  this  red,  tiiat  red  and 
for  any  red,  and  fo  also  with  green ;  but  when  we  say  tliis  red,  or  this  or  thai 
green  we  mean  an  individual.  And  lience  in  heterical  propositions,  Ihelerni:* 
are  individual  names,  Ahile  in  differential  propositions,  they  are  unlimitfd 
coainion  niimes.  And  we  may  assert  with  truth  that*all  red  is  not  green: 
though  this  proposition,  from  the  custom  of  our  way  of  speaking,  seems  to 
imply  that  some  red  is  green,  and  to  avoid  the  effects  of  language  upon  our 
mind?*  it  is  usual  and  better  to  siy  that  xo  red  is  green.  We  are  accustomed 
to  say  with  truth  that  till  men  are  not  black,  i.  e.,  one  of  the  gregaria  sineqn.i 
non  of  man  is  not  black,  i.  e.,  black  and  each  of  the  gregaria  sine  (pia  non  of 
man  are  differentia,  and  therefore,  by  implicaliou  wo  afflrm  that  some  ir.ca 
are,  or  may,  be  black.  And  hence  the  custom  of  language,  when  we  say  that 
all  red  is  not  green,  would  lead  us  to  inter  that  we  meant,  some  red  is  grcin, 
i.  e.,  that  some  red  and  green  are  homon*  In  every  r  roposition,  therefore,  in 
w  hich  the  particle  not  occurs,  and  the  subject  and  predicate  are  simple  exis- 
tances,  if  the  teims  are  unlimited  common  nomes,  the  proposition  is  differen- 
tial, it  they  are  particular  names  the  prooosiijou  is  heterical;  :is  John  is  not 
(.'liarles.  And  this  is  tilso  the  case  when  both  the  subjectl  ami  preilicate  are 
aggregate  existences,  as  a  man  is  not  a  horse.  Is  a  differential  proposition  ; 
This  man  Is  not  that  <W)g,  heterical.  When,  however,  the  subject  is  an  aggre- 
gate exi8teiice  and  the  predicate  a  simple  one.  Some  further  explanation 
?*fems  necebsary.  Take  the  propo«iti(Ui  snow  is  not  black.  This  proposition 
may  Ik?  thus  stated:  Each  gregarium  of  snow  an<l  bla/k  are  diflerentia.  No 
hnow  is  bbick  means  the  same  thing,  and  {ruardiiig  Hgainst  the  cust<m\  of 
language,  we  may  say  that  all  snow  is  not  bhick ;  better— No  snow  is  black. 
All  these  propositions  mean  Ihe.saiiK;  thing.  All  snow  is  white  means  that 
one  of  the  gregaria  sine  f|U:i  non  of  snow  and  white  are  homon;  but  n<» 
snow  is  black,  means  that  each  gregarium  of  snow  and  black  are  ditlerentia. 
And  hence  in  all  pr()poiiti.ins  no  is  always  the-^ii^n  o**  differentiation. 

None  is  equivalent  to  xo  one,  of  which  words  it  is  compounded  ;  and 
when  we  K;iy  that  none  of  the  horses  are  gray  we  mean  that  xo  one  of  the 
horaes  is  gray,  i.  e.,  gray  and  the  color  of  any  one  of  the  horses  are  differentia. 
Xo  one  of  the  horses  is  gray,  hoiivever,  is  a  very  different  proposition  in  its 
terms  than  xo  horse  is  gray,  i  e.,  each  gregarium  of  any  horse  and  ^iray  are 
differentia. 

We  here  subj<»in  a  few  examples  fur  practice:  A  river  is  not  an  ocean; 
nn  Indian  is  not  a  negro;  an  apple  is  not  a  peach  ;  lio  fish  is  a  bird  ;  a  gosling 
is  11(4  a  «^hieken ;  gunpowder  Is  not  saltpeter;  steam  is  not  water;  none  of 
the  pupils  are  Irruned  ;  a  true  christian    is  nwt    vicious;  cotton    is   not    wool; 


66 

iron  is  not  explosive;  day  is  not  night;  cause  is  not  effect;  no  horse  is  a  stone; 
the  laiubow  is  uot  a  cloud;  no  color  is  a  sound;  the  rocks  are  not  trees.  «fcc. 

CHAPTEIi    XIV. 

COM  MENSURAL   rKOI*()i*ITIONB. 

Having  treated  of  the  first  four  classes  (»f  propositions,  we  come  now 
to  commensural  propositions.  It  must  Ix?  evident  to  any  one  that  if  we  take 
two  simple  existences  wfticli  are  inter  se  ditlerentia,  white  and  green  for  in- 
stance, we  can  not  truthfully  say  that  they  are  iu  any  respect  related  to  each 
other,  except  as  colors;  indirectly,  as  colors,  they  arc  similia,  but  directly, 
they  are  inter  se  diflerenlia.  lielween  two  such  existences,  therefore,  no  com- 
parison can  be  made  by  whicli  a  result  other  than  an  heterical  or  ditt'erenlial 
one  can  be  attained.  Tliey  are  not  similia  and  iheretore  we  can  not  by  their 
comparison  obtain  a  similical  result;  nor  from  their  comparison  can  we  ob- 
tain homon.  After  hiving  obtained  therefore,  the  results,  homou,  hetera, 
similia  and  ditfereniia,  in  order  to  obtain  propositions,  which  will  remler 
results  dift'erent  from  those  just  mentiontd,  we  must  measure  iater  se  results 
already  obtained.  But  hom«)n  can  not  be  measured,  for  it  is  an  identical 
thing,  and  a  thing  to  be  measured  must  be  measured  by  some  other  thing. 
JJul  hetera,  as  hetera,  can  not  l>e  measured,  for  in  measurement  there  must  lie 
siome  coincidence  anil  not  mere  separation,  and  differentia,  as  differentia,  can 
not  be  measured,  for  they  can  have  nothing  iii  common  which  is  measurable. 

^^imilia,  therefore,  are  the  only  results,  which  admit  of  c<miparative 
measurement.  We  can  say  that  this  red  is  as  red  as  that  red,  i.  e.,  this  red 
:iud  that  red  are  conuuensural,  and  if  we  compare  one  slick  with  another  we 
can  say  that  this  stick  i>'  as  long  as  that  one  I.  e.,  the  lengths  of  the  two  sticks 
are  commensural,  and  thus  we  can  compare  n»any  of  the  similia  of  nature 
and  obtain  commensural  results.  We  do  not  lUem  it  necessary  to  enlarge 
upon  the  subject  ol  commensural  propositions,  as  we  coneluded  that  tliey 
will  be  easily  under-^to«>d,  and  they  will  als«i  be  illuslratid  along  with  the 
iuhers  hereafter.  We  must  here  observe,  how  ver,  that  homon  is  at  the  bot- 
tom cf  them.  Wi»en  we  say,  this  red  is  as  red  as  that  reil,  the  a8  iikd  an«i 
THAT  red  are  houion,  and  by  stating  two  homonical  propositions  with  tin* 
word  AS  between  them,  we  will  readily  see,  how  tw«  hom»)nical  propositions 
merge  into  one  commensural  one:  Thus,  this  red  is  red,  as,  that  red  is  r«f«l. 
In  the  first  pr(»position,  the  subject  and  p:edicate  are  objecliontly  homon, 
and  so  also  with  the  second  proposition,  and  the  word  as  shows  that  the  two 
are  commensural.  W<'  will  sulijoin  a  tVw  examples  (or  practice:  The  day 
WHS  as  dark  as  niixhl ;  this  candle  shines  as  bright  as  thul  one;  she  looks  as 
fresh  as  the  rose;  it  is  just  as  sweet  as  honty.     x^-;  — /. 


6? 
CHAPTER  XV. 

IXCOMMKNRCUAL   PROPOSITIONfl. 

We  come  now  to  the  consideration  of  incommensurable  propositions, 
the  last  class  of  logical  propositions.  And  in  incommensural  propositions, 
the  existences  compared  are  similia  in  kind,  but  they  differ  iu  decrree  or 
quantify.  \^hen  we  say  that  this  candle  shines  brighter  than  (hat  one,  we 
mean  (hat  there  is  an  excess  of  brightness  in  the  one  compared  with  the 
other.  The  two  are  not  differentia,  as  wliite  and  black  are,  bi.t  there  is  a 
difference,  an  excess,  in  the  one  over  and  above  the  brightness  which  exists 
in  the  other.  The  difference  In  the  specific  gravity  of  bbdies  is  expressed  in 
incommensural  propositions,  as  ijold  is  heavier  than  iron,  i.  e.,  the  specific 
gravity  of  gold  and  (hat  of  iron  are  incommensural.  This  excess  in  one  of 
the  existences  compared  is  some  times  shown  by  the  use  of  an  adjective  name 
in  the  comparative  degree.  There  are,  however,  three  ways  of  expressing  the 
exc(»sg  in  words,  viz.,  A  is  larger  than  J5,  li  is  less  than  A,  ai.d  B  is  not  so 
large,  or  not  as  large  as  A. 

Now  when  we  say  (hat  snow  is  white  i.  e.,  one  of  the  facial  gregaria  of 
snow  and  white  are  nomon,  we  l.K-ate  the  gregarium,  white  among  the  other 
gregaria,  which  make  up  snow,  so  when  we  say  that  ice  is  colder  than  water, 
we  locate  the  existence,  which  would  t)e  named  by  the  adjective  name  In  (he 
I  osiiive  degr^H?  in  the  subject  ice,  ami  by  adding  eh  or  mohk  (o  (liis  adjecdve 
name,  and  thus  marking  an  excess,  we  locate  hIso  the  excess  in  the  subject. 
Take  first  (he  case  of  the  comparison  of  simple  existences,  this  red  is  retler 
than  (hat  red.  Now  leaving  kh  off  of  the  adjective  name  and  we  will  have 
HEKoiiE  TiiKM,(his  red  is  red,  an  homonicnl  proposition.  And  in  (he  propo- 
sition (his  led  is  reder  than  that  red,  we  retain  the  homonical  red— the  predl- 
eate  of  the  homonical  proposition,  and  add,  v.n  to  its  name  to  snow  an  excess 
al»ove  the  retl  which  follows  after  tuan,  and  which  is  ihe  predicate  of  (he  in- 
(ommensural  |>rop<.sllion.  Hut  as  (he  predicate  of  the  luunonical  proposition, 
was  hn-aied  objectively  in  the  subject  (.f  the  proposition,  i.e.,  it  and  tne  subj<^ci 
were  found  (o  be  homon, so  (he  excess  ridded  lo  it  in  the  incommensural  pro- 

poslilon  must  be  located  with  il  in  the  subjeei  of  the  incommensural  uroiH.- 
situui.  *^     * 

In  the  incommensural  proposition,  this  red  is  less  reil  than  that  red, 
however,  the  «lecremenl  is  li»CM(ed  in  the  subject  and  conwquenlly  the  excess 
IS  in  the  |»redicate.  And  In  the  pro|)08ition,  this  red  is  not  so  red  as  tlint  red, 
the  f-oKii)  aijfl  THAI.  KKD  are  h«  mon,  i.  e.,  the  degrees  o[  red  suujeciively 
(oinmensural  are  objectively  hcmion  in  ti.e  predicate  of  the  incommensural 
propo.sitiop,  and  the  particle  ^'(»T^h<^ws  that  the  degrees  in  the  subject  and 
those  in  the  homonical  predicate  are  ineommensuial.  In  the  commensural 
pr<vposilien,  this  red  i«>  as  rcti  as  that  red,  the  last  (rtOREi>s,  which  are  h'>m<m 


68 

in  il»e  prcdicHlo.  and  the  subject  are  commensural,  but  if  we  insert  not  we 
will  have;  lliis  re<l  is  not  as  reil  as  that  retl,  in  wliich  the  last  two  reds  are 
liomon,  and  their  degrees  and  tiiote  of  the  subject  are  inconimensural,  the 
ditferepce  or  excess  being  lo  the  predicait. 

Now  when  the  lubject  is  au  aggrejfate  existence  and  it  it  compared 
apparently  with  ;in  aggregate  existence  in  the  predicate,  in  commensural  and 
incoinmensural  propositions,  it  is  always  one  of  the  gregari*  of  each  that  i^ 
compared,  and  these  grr  garia  compared  are  always  similia  in  kind,  but  commen- 
sural or  incommensural  in  decree.  In  the  proposition  si»ow  i»  whiter  than  chalk 
the  facial  gregariuni,  while  exists  in  each  of  the  aggregate  exinlenees,  but  the 
degrees  of  white  in  the  one  and  in  the  other  are  compared  and  foun<l  to  be  in- 
rommensura.  And  when  we  say  all  snow  is  whiter  than  chalk,  it  is  one  of  the 
gregnria  sine  qua  non  of  snow  that  enters  into  the  incommensural  proprtsillon. 
Ana  if  we  could  say  in  truth  that  all  snow  is  whiter  than  all  or  any  chalk, 
the  degrees  ne  plus  ultra  <»f  chalk  would  be  compared. 

Before  passing  on  to  the  next  chapter,  we  must  examine  such  pro|>osi- 
lions  as;  John  is  the  strongest  man  in  the  house.  This  proposition  at  first 
sight  would  apfjear  to  lHt>ng  to  a  seventh  class  of  propositions,  but  on  exami- 
nation,  it  will  be  found  to  In?  merely  an  homonical  proposition  collected  into 
a  conclusion  from  several  incommensural  <»nes,  and  it  may  be  thus  staled,  the 
strongest  man  among  t lit  men  m  the  house  and  Jidin  are  homtm.  And  so 
ulso,  Sampson  was  the  strongest  man  of  whom  we  have  read,  is  an  homonical 
propositiou.  Hercules  was  stronger  man  Sampson,  is  an  incumiuensural  pro- 
position. And  all  propositions,  in  which  there  are  superlative  names,  are 
homonical.  We  g.ve  the  following  examples  fur  practice:  Winter  is  colder 
thau  summer;  the  elephant  is  m«)re  intelligent  than  the  as"* ;  dogs  are  nwue 
taithfui  than  cats;  c<»ws  are  more  useful  than  rabbits;  the  bite  of  a  rattle- 
snake is  mme  dangenms  to  man  than  the  atingof  the  wasp;  Honey  issweeter 
thansuirar;  the  m>le  of  the  nighleni'ale  is  more  plettsaul  than  ihht  t»f  the 
ei\»\v :    x-f.. ^/., 

CIIAPTKH  XVI. 
PROi'osiTioNs  i»uo.Mis<r<)i;»i.v. 

Having  ;^'ono  through  with  the  six  classes  of  propositions,  we  should 
next  in  order  consider  their  subdivisions  into  ctitegorieal  an«l  hypothelieal ; 
we  do  not  deem  it  necessary,  however,  to  do  more  Ihan  mention  Ihesesubdivi- 
sioiis.  Kvery  u\w  will  see  for  himself  that  any  pripositioc  of  either  of  the 
foregoing  classes  mny  be  staled  ealegorieally,  i.e.,  the  result  be  aftirmed  as 
Metunlly  existing,  or  a  re-ult  may  lie  siippo<M>d  lo  ex'st  for  the  sake  i>f  argn 
ment.  We  will  therefore,  now  give  ^ome  further  attention  to  the  terms  and 
c<»pula  of  pro|M»siiions  ol  all  the  foregoing  classes. 

Ami  lookinir  back  to  the  nominal  iruihs  groundid   in   the  non-ego,  of 


I  G9 

which  we  spoke  at  the  beginning  of  our  iiirosligalious,  anJ  supposing  that 
all  objects  had  had  the  same  color,  cojld  we  have  called  this  nominal 
tiulh  A  (one)  color?  We  have  already  shown  that  the  unit  is  a  numerical  re- 
lation and  that  our  knowledge  ot  Ills  envolved  from  duality  or  plurality-. 
And  in  the  five  nominal  truths  mentioned,  we  have  hetera,  from  which  the 
knowled;«:e  of  first,  SECOND,  thikd  ^kc,  might  have  beeu  evolved.  JBut 
we  have  also  shown  that  when  numbers,  the  names  of  the  individuals  of 
hetera,  or  of  commensural  colligations  of  hetera,  are  applied  to  existences, 
and  the  name  to  distinguish  individuals  otherwise  than  helerically,  is  spoken 
or  written  after  them,  the  name  so  spoken  or  written  must  be  the  name  of 
similia,  a  common  name.  We  may  hi^ve  a  horse  and  a  dog  and  the  two  aro 
existences.  But  exisienck  is  not  a  name  given  lo  distinguish  existencea 
inter  se,  and  should  we  write  any  name,  which  does  distingui:>h  existences 
inter  se  alter  the  word  two,  we  will  find  that  two  will  not  apply  unless  the 
existences  be  inter  ss  similia.  Horse  and  dog  are  dillerentia,  and  their 
names  distinguish  them;  neither  of  these  names,  therefore,  can  be  written 
after  two  so  as  to  express  lo  us  the  numerical  sum  of  a  horse  and  a  doir:  as 
hetera  existences,  two  may  l>e  applied  to  them,  but  not  as  ditterentia. 

And  respecting  the  nominal  truths,  as  tiie  are  inter  se  difterentia,  two 
could  not  be  joined  with  any  name,  which  distinguishes  them  as  nominal 
iruths.  But  if  oxic  be  the  name  of  a  numerical  relation,  as  we  have  shown 
when  it  is  applied  to  a  dirt'erential  name,  there  must  be  more  than  one  thiu'^' 
(lislinguished  in  like  manner  by  the  same  name;  there  must  bo  similia; 
otherwise  the  ihing  distinguished  oy  such  name  could  have  no  numerical  re- 
lations to  other  things,  except  as  hetera,  which  in  language  do  not  receive  differ- 
eulial  names,  which  afterwards  become  Ihecommou  names  of  similia.  And 
therelore,  when  we  say.  An  existence,  by  this  expression  we  show  that  we 
have  in  our  mind  one  of  several  or  many  existences,  i.  e.,  one  of  hetera,  and 
\\heu  we    say  a  dog,  the  expression  shows  that  we  mention  one  of  similia. 

Looking  then  at  the  nominal  truth,  (oi.oii,  could  we  say  that,  this  is  a 
(one)  color?  We  think  not.  We  could  say  this  is  color,  or  this  is  an  exis- 
tence, and  that  is  sound;  but  a  color,  as  a  name,  not  only  distiuiruishes  color 
from  sound,  taste,  d'C,  but  it  also  points  out  some  one  of  similia,  as  colors. 
And  hence  a  or  an  before  a  name,  in  homonical  propositions,  makes  them 
(luasi  similical ;  as  this  town  is  a  Philadelphia,  i.  e.,  this  town  and  one  of  the 
IMiiladelphias  are  homon,  and  in  effect,  this  town  and  Philadelphia  are  simi- 
lia. The  proposition  This  town  is  Philadelphia;  is  an  homonical  pr«po8itioa 
but  the  placing  of  a  before  the  predicate  makes  the  proposition  tnoiigh  ho- 
monical still,  quasi  similical,  there  being  but  one  Philadelpnia  in  our  mind, 
and  this  t<»wn  not  being  that  one. 

And  all  names  excepting  proper  names,  used  as  terms  of  propositions 
point  out   among  other  things,   a  numerical   relation   inter  similia.    In   the 


70 

l.omonlcal  proposilion,  John  U  Joh.. ;  neither  of  llie  ierm=i  p>inl  out  a  nu- 
merical relation;  but  in  the  homonicail  prop:)sitiou  J  .hn  is  a  man;  i.  c.,Joha 
anil  a  (one)  man  are  homon,  ihe  predicate  term  i  oin'.s  out  a  numerical  rela- 
tion, and  as  it  stands  lor  tl»e  8ame  object  as  John,  when  John  is  brought 
among  the  similia  of  which  it  is  one,  among  these  objects.  John  has  a 
numerical  relati»m,  he  is  a  man,  one  of  the  simiiia  named  man. 

Now  bringing  before  us   again  the   name   color,  i.»*  these  existed  a   reil 
and  A  green,  we  would  tJien    have  two  colors  and  we  could  say  that  re<l    is  a 
color  and  also  that  green  is   a  color;    but    upon    the  principle  just  exhibited 
^nbi.ve  were  there  but  one  red  object   and  one  green   object  in   existence,   ie«l 
and  green  tjvould  be  pro|>er  names  anil  we  coi  hi  not  say,  this  is  a  red,  or  that 
is  A  green,  though  we  could  say  this  is  a  red  color  antl  that  is  a  green  color. 
Jiut  hi  the  homonical   proposition  Ukd  is  a  color;  uki>  is  brought  from  pri- 
mary proposili«»nal  truths  into  noiuinal  truths,   and  among  nommal  truths,  it 
is  one  4.f  the  simiiia,  a  color,  i.  e.,  ukd  and  a  (o.ie)  color  are  liomon.     Hut    if 
HKD  be  A  color,  ho^  can  we  fully   distinguish  m  every  respect  this  existence 
liiim  others  by  words,  when  Ae  have  it  in  our  minds,  olherwiiC  than  by  cal- 
ling it  a  ukd  color  r    And  hence   we  see   that  every  term   of  a   proposilitm, 
which  is  made  up  of  more  than  one   name  of  simple  existences,   |>oinls  out 
the  results  of  several  relatims,  ami   the   numerical   relation    among  simiiia 
pointed  out  by  the  term,  is  called  the  extension  ot  the  term. 

Passinir  on  now  to  the  consideration  of  terms,  which  are  the  names  of 
aggregate  existences,  take  the  piopoj-iiion,  »now  is  while;  i.  e.,  a  gregarium 
iiflinow  and  a  white  color  are  honwui,  and  we  see  that  wuitk  is  brought 
into  and  fasciculated  among  other  gregaria  in  snow  by  an  homonical  pro- 
p».8ition.  Again,  Snow  i-  cold,  Snow  will  mell,  iVc,  are  all  hom(»nical  pro- 
p«»sitions,  and  the  prwlicftes  of  all  these  i  roposii ions  are  located,  lasciculaled 
in  sni)W.  We  may  say  While  is  in  snow ;  i.  e.,  the  where  of  a  wiiitk  and  thai 
of  snow  are  homon.  Cold  is  in  snow,  The  capacial  gregarium  of  melting  is  ia 
huow;  all  those  gregaria  co-exist  in  snow,  i.  e.,  a  fasciculus  of  certain  grega- 
ria  and  snow  are  homon.  And  if  by  homonical  propositions  we  fasciculate 
simple  existence^*  in  an  aggregate  one,  can  we  not  in  like  manner  bring 
together  aggiegate  existences?  When  we  say.  The  audience  was  intelligent, 
we  have  done  so.  John  is  mlelllgent,  V\  illiam  is  inlelligen:,  Mary  is  intelli- 
gent, A:c. ;  but  John  was  one  of  the  audience,  William  was  one,  A:c. 

And  when  a  name,  as  t'le  term  of  a  proposition,  stands  for  an  aggregate 
existance,  the  gregaria  taken  together  in  iasciculo  constitute  what  is  called 
Ihe  comprehension  of  the  term.  And  in  the  ditlVrential  proposition,  Stone 
•  is  not  iron,  the  comprehensions  <»f  the  terms,  stone  and  iron,  i.  e ,  the 
gregaria  of  the  one  and  those  of  the  other,  arc  compared  in  fa-sciculo.  S<mie 
of  the  gregaria  of  the  one  and  some  of  the  other  may  be  simiiia;  but  if  the 
one  comprehend    certain   gregaria  and    the    other  certain   gregaria,  which 


71 

are  inter  se  differentia,  or  if  the  one  contain  gregaria  over  and  above  tke 
sum  o(  the  gregaria  contained  in  Ihe  other,  the  two  fasciculi  are  inter  se 
differentia,  and  they  are  differentia  throughout  the  whole  extent  of  the 
simiiia  of  the  one  and  of  the  other.  Stone  is  not  iron  is  equivalent  to,  All 
sfone  is  not  iron ;  belter,  No  stone  is  i»on ;  and  this  proposition  is  equi?  l-nt  to 
No  iron  is  stone.  And  hence  when  fasciculi  of  gregaria  comprehended  by 
the  subject  and  predicate  terms,  are  compared,  the  proposilion  may  always 
be  converted,  i.  e.,  the  gubject  be  umde  the  predicate  and  the  predicate  the 
subject.  This  is  also  the  case  when  simple  existences  are  compared.  Ked  is 
red,  homonical ;  This  is  not  that,  That  is  not  this,  heterical ;  Red  is  not  green, 
(ireen  is  not  red,  differential ;  This  is  like  that,  That  is  like  this,  similical ;  This 
red  is  as  red  as  that.  That  red  is  as  red  as  this,  comniensural ;  ana  This  red  is 
not  so  red  as  that,  That  red  is  reder  than  this,  Incoramensural.  But  wh^'u 
one  term  is  t  le  name  of  an  aggregate  existence  and  the  other  the  name  of  a 
simple  existancc,  it  is  always  one  of  the  gregaria  of  the  aggregation  that  is 
ccmipared  with  the  simple  existence  pointed  out  by  the  other  term,  as  we 
have  already  seen:  Snow  is  white,  means  thai  the  color  of  snow  is  white 
which  may  also  be  converted  into  Whitk  is  the  color  of  snow.  John  is  a 
man,  may  be  converted  into  One  man  is  John.  And  hence  in  order  to  ascer- 
tain the  existences,  whicn  are  really  compared  in  any  proposition,  construct 
one  of  the  terms,  if  necessary,  so  that  the  terras  may  then  be  transposed  and 
give  the  same  result  as  before.    Tnis  may  l)e  none  in  all  propositions. 

Now  pre|H)siiiou8  as  we  have  heretofore  said,  are  names  of  relations 
in  space  ainr)ng  existences:  thus  when  we  say  Snow  is  white,  we  mean  that 
the  color  of  snow  Is  while,  and  snow  beiog  the  name  of  a  faciculus  gregaria, 
OF  shows  that  colok  is  located  as  one  among  the  gregaria  in  fasceculo  dis- 
tinguished by  the  word  snow:  it,  that  is  the  preposition  of,  is  Ihe  name  given 
to  the  relation  of  color  among  the  other  gregaria  in  space.  And  hence °h«re 
is  no  difference  of  affirmati<m  between  Snow  is  white,  and  The  snow  upoa 
ihe^mountain  is  white;  the  affirmations  are  simiiia.  But  in  the  latter  pro- 
position Oneot  the  gregaria  of  snow  upon  the  mountain  is  white;  in  the 
subject  we  have  a  numerical  relation  (one)  existing  among  simple  existences 
(gregaria)  located  ia  an  homonical  wiikkb  (in  snow)  and  named  snow,  which 
wiiEKR  is  objectively  Homonical  with  another  wheke  indicated  by  Upon  the 
mountain.  But  a  (one)  is  not  the  existence  compared  with  white;  the  name 
AVHiTE  is  differentia;  one  distinguishes  helera  and  points  out  the  relation 
among  simiiia,  while  the  proposition  is  homonical;  neither  is  any  where 
compand  with  wjjitb,  for  where  and  white  are  differentia,  while  th»! 
proposition  is  homonical;  snow  is  not  compared  with  white,  but  the  color  of 
snow;  nor  is  the  mountain  compared  with  white;  there  is  nothing,  therefore, 
in  either  of  the  foregoing  propositions  compared  with  white  besides  a  color. 
All  the  words,  therefore  One  of  the  gregaria  of  the  snow  upon  the  mounUiin; 


■? 


taken  togelher,  const  itulc  but  one  name  to  ilisllnguTsh  one  simple  existence 
in  every  respect  from  otliers,  ami  wiiicli  simple  exiitencu  we  compare  wilU 
UHITE  Jind  pronounce  tiiem  to  be  objoclively  ln>mon. 

If  a,  b,  e,  d  and  e  be  th ;  simpU'  existences,  the  grogaria  of  an  ajr^re- 
gate  existence,  and  A  be  the  name  of  the  rascioulat'd  gregaria,  we  may  then 
sajr  according  to  the  custom  of  lani^uai^e  that  A  is  a,  A  is  b,  etc.  And  if  we 
wish  to  locate  A  in  a  some  wiiekk,  wliich  shall  be  distinu'uished  from  other 
WUERES  by  words  we  m;*y  say;  A  upon  the  tabb;  is  a.  And  if  the  where  is 
n«»t  ycl  sufficiently  distinguished,  and  we  may  say,  A  \  pon  the  table  in  the 
house;  and  still  further,  A  upt>n  thr  table  in  the  Iidusc  of  Jfdm  Sliles  on 
front  street  between  Walnut  and  CMiestnut  streets  in  ll>e  city  of  I'hlladelphia 
is  A.  15ul  again,  take  the  proposition,  John's  book  is  on  the  table;  and  we 
see  that  the  ftubjcct  of  tliis  proposition  i>  a  fasciculation  of  the  subject  and 
jjredicale  of  the  proposition,  Tiiis  book  is  the  property  of  John.  We  do  not 
consider  it  necessary  to  explnin  tlie  terms  of  propositions  further:  but  the 
copula  i»  yet  to  be  examined. 

Now  in  tlie  propositions,  I  am;  1  exibt,  or  I  am  an  existence:  we  must 
see  that  the  attirmalion  is  made  in  the  pres>ent  tense,  granuaatieally.  And 
in  the  proposition,  I  was,  Did  exist,  or  Was  an  existence;  the  affirnmtion  is 
also  made  at  the  present  lime,  but  tlie  time  of  existence  spoken  of,  is  the 
past.  I  was- an  existence;  may  be  rendered,  The  lime  of  my  existence  of 
which  I  spvak,  and  past  time  are  hoiaon.  C*idumb  u  iljscovered  America,  A 
1).  1493;  may  be  rendered  The  time  of  the  discovery  of  America  by  Colum- 
bus aiui  A.  D  141)2  am  homOn,  etc.  And  whatever  may  be  the  tense  of  tha 
Vfirb,  the  existences  are  always  compared  and  the  attirmation  made  at  the 
present  lime.  But  respecting  what  is  called  tlur  potential  mode  by  gram- 
marians, as  John  may  be  a  scUidar;  the  verb  itsrlf  imprus  ::apacial  gregaria; 
the  cspacial  gregaria  of  John  and  those  of  a  scholar  aresimilia;  and  iu  the 
pro|MH»ition,  John  might  have  been  a  scholar;  the  capaeial  gregaria  are  rc- 
fered  to  as  having  existed  in  past  time. 

« 

Now  in  all  propositions,  we  say  that  the  c«>i)ttla  is,  means  exists  But 
take  the  propositicm,  Nothiug  is  nothing;  and  if  is  nicans  exj»f>,  what  Is  it 
that  does  exist,  for  nothing  can  nf)t  be  an  existence?  But  we  say  lUat  it  U 
the  rdalion  l)elween  the  suliject  and  predicate  that  exists.  But  still  it  will  l)e 
asked  the  relation  f>f  what,  when  we  say  Nothing  is  nothing?  And  in  order 
to  nnderstand  this,  it  is  necessary  to  consifler  how  we  came  by  the  name  no- 
thing. Take  the  proposition  This  is  nothing,  i.  e..  This  tl^ng  and  no-tl»ing 
are  homon.  Now  if  the  subject  this  tiiixo,  means  st^me  thino  and  the 
preilicate  x«»thino,  means  no  thing,  how  can  the  two  be  homon  ?  If  we  con- 
ceive of  a  witch,  an  old  ]u\f  of  a  woman,  with  a  beard,  ruling  a  broomstick, 
aubjectiveh  this  is  some  thing,  but   obj(  clively  it  is   nothing,   and  therefore, 


73 
we  can  say  with  truth  that  this  some  thing  grounded  in  the  ego,  is  upon  the 
ground  of  the  non-ego  nothing;  this  is  nothing. 

"Kom.— "Peace,  peace,  3Iercutio,  peace;  Thou  talketh  of  nothing." 
"Marc— True,  I  talk  of  dreams,   wlilcb  are  the  children  of  an  idle 
brain,  begot  of  nothing  but  rain  fantasy.'* 

Now  had  man  gained  the  knowledi^e  of  only  two  objective  existences 
and  had  he  called  the  one  a,  not  a  would  have  been  a  name  sufficient  to  dis- 
tinguish th(*  other,  and  he  then  could  have  said  pointing  to  a   This  Is  a  and 
pointing  to  the  other,  This  is  not  a;  for  if  it  be  not  a,  it  must  be  the  other  ex- 
istence.   Both  these  propositions  then  would  be  homonical  viz:   This  is  a 
this  and  a  arc  homon  ;  This  is  not  a,   this  and  not  a  are  homon.    But  if  lie' 
wished  to  show  a,  and  not  a  to  be  differentia,  or  to  affirm  helera  in  a  proposi- 
tion, he  would  have  to  say,  a  is  not  not  a,  i.  e.,  a  and  not  a  are  hctera,  or  a  and 
not  a  are  diflereutia.    But  if  there  were  four  or  Ave  existences  known  to  man 
and  he  should  distinguish   one  of  them  by  the  name   a,  and  then  pointing  to 
another  he  should  say,  this  is  not  a;   not  a,  would  not   distinguish  any  one  of 
the  remaining  four  from  the  others,  and  consequently  not  a  would  be  indefi- 
nite.   And  hence  when  there  are  two  existences  or  but  two  modes  of  exis- 
tence, and   the  one  is  named    a,  for  instance,  not  a  may  be  used  as  a  definite 
namefortheother.  as  truth,  not  truth-error;   faculty  of  vision,   not   faculty 
of  vision-blind;  hearing,  not  hearing-.ieaf.  A:c.     Bat  when  there  are  more 
than  two  existences   or  modes  of  cxistance,  .not,  i;k,  i.x   dis,  Arc,  joined   to 
names  makes  an  indefinite  name. 

But  suppose  that  we  had  the   knowledge  of  but  two  existances  which 
were  inter  se  differentia,  and  we  should  give  to  each  of  them  a  separate  name 
as  iiED  and  green  for  instance,    we  would  then  say  red  is  not  green.    But  not 
oKEK^^  if  it  be  any  thing,   must  under  the  supposition,  be  red,  and  we  could 
say,  not  green  is  red,  i.  e.,   not  green  and  red   are   homon.    But   if  we  had  a 
knowledge  of  three  diflereutia,   red,  white  and   green,   for   instance,  and   we 
should   say  that   red  is  not   green,  not  green    would  stand  f\)r  either  red   or 
WHITE,  and  would  b«  indefinite.    J5ut  what  definite  existence  Is  meant  iu  the 
casl^by  not (jueen,  would   be  indicated    by  the   subject  of  ihe   proposition. 
RKi),  and  hence  red  and  the  not  (4Rkkn  are  homon.    And  if  not  grekx  and 
RED  be  homon  in  the  proposition,  red  is  not  oreen,  red  and  green  muht  be 
diflereutia:  for  in  this  proposj.irm,   red  and  not  green  are  homon,   and  in  the 
proposition,  green  and  not  red  aie  homon,  green  is,  and  red  is;   the  homoni- 
cal proposition,  red  is  green,  however,  is  not  true,  and  the  slmilical  proposi- 
tion, red    is  like  green  is   also  untrue,  and   hence  nc  see  how   homon  lies  at 
the  loiindAtion  of  ail  propositions;  and  we  see  also  that  the  pai tides  not  and 
NO,  belong  always  to  the  subject  or  predicate  and  never  to  the  copula. 

We  have  yow  g(me  far  enough,  perhaps   to  make  our  n«:ws  of  proposi- 
li<ms  be  understood ;  yet  it  may   be  said  That  when  we  say  snow  is  white  and 


^» 


we  change  the  wording  of  this  proposition  into  One  of  the  gregaria  of  sno  ft 
and  white  are  honion,  we  have  but  changed  a  simple  proposition  into  a 
complex  one; sucli  however  is  not  the  case.  When  we  say  Edward  and 
John  are  good,  we  can  fully  express  in  two  proposition  the  meaning  of  the 
above  phraseology,  as  Edward  is  good  and  John  is  good.  But  when  we  say 
One  of  the,  gregaria  of  snow  and  white  are  homou,  we  can  not  resolve  this 
Into  two  propositions  and  say  One  of  the  gregaria  of  snow  is  the  same  thing 
and  white  is  the  same  thing,  with  any  sense ;  neither  can  we  resolve  This  grain 
of  wheat  and  that  grain  of  wheat  are  similia,  into  This  graia  of  wheat  is 
similia  and  that  grain  of  wheat  is  similia.  And  if  we  are  right  and  we  are 
understood  in  our  views  of  propositions,  we  think  it  will  not  be  difficult  to 
explain  hereafter  the  syllogism  in  all  its  modifications  and  functions. 

CHAPTER  XVII. 

THE  SINGULAIl   SYLLOGISM. 

In  every  legitimate  syllogism,  there  must  be  two  and  only  two  propo- 
sitions, which  are  called  the  premises,  and  a  conclusion  drawn  from  these 
premises.  It  is  also  necessary  that  there  be  four  subjectively  lieterical  exis- 
tences, two  of  which,  one  in  each  premise,  must  be  objectively  hetcra,  and 
two  ot  which  must  be  objectively  homou,  or  similia  or  commensuru  inter  se, 
and  that  the  other  two  apear  in  the  conclusion.  The  name  of  the  homoni- 
cal  existence,  or  of  the  similical  or  commensural  existences,  which  itre  in  the 
premises,  but  not  in  the  conclusion,  is  called  the  middle  term,  because  it 
designates  or  distinguishes  the  homonical  existence  or  the  similia,  or  com- 
iiiensura,  with  which,  each  of  the  existences,  which  appear  in  the  conclu- 
sion has  been  compared,  and  it  is  by  means  of  thi*^  homonical  existence  or 
similia  or  commensura  designated  by  this  tliat  middle  term,  the  comparison, 
between  tha  other  two  existences  is  eftected  and  the  result  set  down  in  the 
conclusion.  Now  it  must  appear  upon  tlie  principle  of  pormutation  that,  if 
a,  b  and  c  be  tlie  terms  of  the  premises,  and  we  arrange  a  and  b  together  and 
a  and  c  together,  we  can  have  four  and  only  four  diflerent  arrangements  in 
the  premises;  thus,  a  b,  b  a  and  a  c,  c  a.  And  hence  logicians  have  divided 
syllogisms  into  four  figures,  as  they  are  called,  according  to  the  positions 
occupied  by  the  middle  term  in  the  premises.  This  middle  term  mav  denote 
the  subjects  of  both  propositions,  or  premises,  the  predicates  of  both,  or  the 
subject  of  the  first  and  the  predicate  of  tlie  second,  or  the  predicate  of  the 
first  and  the  subject  of  the  second.  And  hence  let  a,  or  a  and  a  when  similia 
or  commensura  are  used  be  the  middle  term,  and  the  following  paradigm  will 
show  the  figures : 


1st  figure. 

2d   figure. 

'6i\  figure. 

4th  figure. 

A  isB 

B  is  A 

A  is  B 

Bis  A 

C  is  A 

Cis  A 

AisC 

A  is  C 

.-.G  is  B 

.-.(?  is  B 

.-.C  is  B 

.-.C  is  B 

75 


%  Now  if  we  take  the  first  four  classes  of  propositions  these  may  be 

combined  two  and  two  as  premises,  and  hence  the  first  figure  will  give  six- 
teen MODES  of  syllogising  according  to  the  different  manner  in  which  wo 
combine  these  four  classes  of  propositions  and  so  with  the  other  figures. 
The  following  paradigms  will  show  the  manner  of  combining  the  first  four 
classes  of  proposition^  in  all  the  figures : 


FIRST  FIGURE. 


First  mode. 

A  &  B  are  bomon, 

C&A'    "     homon. 

.*.  C  &  B  "  Bimilia. 


Second  mode. 

A  JK;  B  are  hetera, 
C  &  A  are  hetera, 
.*.  C  &  B  are  hetera 


Third  mode* 

A  &  Bare  similia 
C  &  A  are  si  nilia, 
.\Q  &,B  are  similia. 


6th. 
A  &  B  are  liomon, 
0  &  A  are  hetera, 
.-.  C  &  B  are  hetera. 


8th. 

A  &  B  are  hetera, 
C  &  A  are  homon, 
.-.  C  &  B  are  hetera. 


Fourth  Mode. 

A  «&  B  are  differentfa, 
C  «&  A  are  differentia, 
.'.  C&B  '♦  differentia, 
or  similia. 


6th. 

A  &  B  are  homon, 
C  &  A  are  similia, 
.*.  C  *fc  B  are  similia. 


9th. 

A  &  B  are  hetera, 
C  &  A  are  similia, 
.-.  C  &  B  are  similia  or 
difllerentia. 


7th. 
A  »fe  B  are  h«mon, 
C  &  A  are  differentia, 
.-.  C  &  B  are  differentia. 


llth. 

A  &  B  are  similia. 
C'  *!t  A  are  homon, 
.'.  0  *k  B  are  similia. 


14th. 

A  &  B  are  differentia. 

(^  »fc  A  are  homon, 

'.  O  it  B  are  difterentia. 


12th. 

A  &  A  arc  similia, 
C  vV:  A  are  hetera, 
.*.  C  &  B  are  similia 
difterentia. 


or 


loih. 
A  &  B  are  differentia, 
C  &  A  are  hetera, 
.-.  C  cV  B  are  differentia 
or  similia. 


10th. 

A  &  B  are  hetera, 
C  «fc  A  are  differentia, 
.*.  C  «fe  B  are  difterentia 
or  similia. 


13th. 


A  &  B  are  similia, 
C  &  A  are  difterentia, 
.'.  C  &  B  are  difterentia. 


16th. 

A  «fc  B  are  dift'erentia, 

C  &  A  are  similia, 

.*.  C  &  A  are  differentia. 


MODES  OF  FIGURE  SECOND. 


1st. 


2nd. 


»  A  A  arc  homon,  ;  B  &  A  are  hetera, 
*  f,  '^'«"  *'!»'•'«'  !  C  dfc  A  are  hetera, 
.-.  C  &  B  •»  similia.  \  .-.  c  &  B  are  hetera. 


3rd. 

B  &  A  iire  ilmllia, 
0  &  A  are  similia, 
.-.  C&  Bare  similia. 


B  «S;  A  are  differentia. 
C  «fe  A  are  differentia. 
.-.  C  &Bare  diff.or  sim 


76 


5th. 

B  &  A  are  homon, 
C  ^  X  are  hetera, 
.*.  C  &  B  are  hetera. 

8th. 

R  &IA,  are  helcra, 
i'  di  X  are  Iioinon, 
.*.  C  A:  B  are  hetera. 

lUh. 

B  (Jb  A  are  similia, 
C  A:  A  are  homoii, 
.-.  ('  &  B  are  sin* ilia. 


Gth. 

B  it  A  are  horaon, 
C&  A  are  similia, 
.'.  C  &  B  are  similia. 


9th. 

B  &  A  are  hetera, 

C  <&  A  arc  similia, 

.'.  V  «fc  B  are  sim.  or  diff. 


7lh. 

B  &  A  arc  Ijomon, 
C  &  X  are  diflereutia, 
.'.  C  (&  B  are  differentia. 


10th. 

B  «&  A  are  hetera, 
C  &  A  are  difl'erentia, 
.',  C  &  B  are  diff.  or  sim. 


14th. 

B  »k  X  are  differentia, 
('  iV  A  are  homon, 
.-.  C  *&  B  are  differeiUia, 


I  12lh. 

'  B  &  A  are  similia, 

I  C  &  A  are  hetera, 

i  .'.  C  »S:  B  jire  sin),  or  diff. 

15th. 

B  it  A  are  differentia, 

V  &  A  are  hetera. 

.-.  V  &  B  are  ditl*.  or  sim. 


13th. 

B  &  A  are  similia, 
C  &  A  are  differentia, 
.'.  C  «t  A  are  differentia. 

16Ui. 

B  &  A  are  differentia, 
C  «.t  A  arc  similia, 
..C&  Bar'e differentia. 


moi)f:s  of  fiot'uk  xninn. 


1st. 

A  X'  H  nr;;  homon, 
A'  Jt  (;  art!  iioinon. 


2nd. 


A  A  B  are  hrtera, 
A  Jt  C  n  V  hettrrti. 
.-.  O  «!t  B  are  hetera. 


:jrd. 

A  A  B  are  xtmflia. 
A  &  r  arc  .imlllH, 
.*.(.'  &  Ban? similia. 


4th. 

A  it  B  are  «Hff«'rentla, 
A  A-  Care  dlirprentla. 
.'.  V  Jb  B  are  diflT.  or  nini. 


5th. 

A  tt  B  tire  homon, 
A  it  ('  are  hetera, 
.'.  A  it  B  are  hetera. 

8th. 

A  it  B  are  hetera, 
A  it  (J  are  homon, 
.'.  ('it  B  are  hetera. 


Gth. 


lllh. 

A  it  B  are  similia, 
A  it  ('  are  homon, 
.'.  ('  it  B  are  similia. 

14tli. 


A  it  B  are  homon, 
A  iV:  C  are  similia. 
.-.  V  it  B  are  similia. 

9th. 

A  it  B  are  hetera, 

A  iV:  (.are  similia, 

. .  ('  A'  B  are  sim.  or  diff. 

12  h. 

A  it  B'are'siniilia, 

A  it  ('  are  helera. 

.'.  ('  it  B  are  snii.  or  diff. 

15lh. 


A  it  B  are  differentia,  '  A  it  B  are  differentia, 

A  it  (?  are  homon,        '  A  it  C  are  helera, 

.-.  V  &  B  are  differential  .-.  C  it  B  are  diff.  or  sim. 


7th. 

A  it  B  are  homon, 
A  iV  U  are  differentia, 
.'  ('it  B  are  differentia. 

10th. 

A  it  B  are  hetera, 
A  A'  ('  are  difterenlia, 
.*.  ('  it  B  are  «liff.  nrsim. 

13th. 

A  it  B  ar<*  similia, 
A  tt  Care  ditterentla, 
. .  (;  iV  B  are  ditlereiitia. 

IGlh. 

A  it  B  are  differentia, 

A  it  (*  are  similia, 

.•.  ('it  B  are  diti'erentia. 


^ 


77 


MODES  OP  FIGURE  FOURTH. 


Ist 

B  and  A  are  homon, 
A'  aud  C  are  homon, 
.-.  C  aud  B  are  aimilia. 


8d. 

B  and  A  are  hetera, 
A  and  C  are  hetera. 
.'.  C  &  B  are  hetera. 


A  andB  are  similia, 
A  and  C  are  similia. 
.*.  C&  Bare  similia. 


4th. 


B  <fe  A  are  differentia, 
A  &  C  are  differentia, 
.-.  C&  Bare  diff.  or  sim. 


5th. 

B  and  A  are  homon, 
A  and  C  are  helera, 
.-.  C  and  B  arc  heiera. 


Gth. 

* 

B  and  A  arc  homon, 
A  and  C  are  similia, 
.'.  C  and  B  are  similia. 


7th. 

B  and  A  are  homon, 
A  and  C  are  differentia, 
.-.  C  and  B  arc  differentia 


8th. 

B  and  A  are  hetera, 
A  and  C  are  homon, 
.-.  C  and  B  are  hetera. 

11th. 

B  and  A  are  similia, 
A  and  C  are  homon, 
.•.  C  and  B  are  similia. 


9th. 

B  aud  A  are  hetera, 
A  aud  C  are  similia, 
.-.  C  &  B  are  sim.  or  diff 


10th. 

B  and  A  are  hetera, 
A  aud  C  are  differentia. 
.'.  C  &  B  are  diff.  or  sim. 


12th. 

B  and  A  are  similia, 

A  aud  C  are  hetera, 

.-.  C  *fc  B  are  sim.  or  diff. 


13th. 

B  and  A  are  similia, 
A  and  C  are  differentia. 
.-.  C  and  B  are  differentia. 


14th. 

B  and  A  are  differentia, 
A  and  C  are  homon, 
.•.  C  &  B  arc  differentia. 


15th. 

B  and  A  are  differentia, 

A  and  C  are  hetera, 

.*.  C  &  B  are  diff.  or  sim. 


IGth. 

B  and  A  are  differentia, 

A  aud  C  are  similia, 

.-.  C  it  B  are  differentia. 


To  the  foreproing  paradigms,  we  will  add  another  in  which  the  existea- 
ces  are  distinguished  by  their  names,  but  without  regard  to  figure. 


1st. 
Snow  is  white— homon. 
The  foam  of  the  seas  is  white— homon. 
Therefore,  the  colors  of  snow  and  of 
the  foam  of  the  sea  are  similia. 


3d. 

The  color  ot  John's  hair  is  like  Ma- 
ry's—similia, 

Mary's  is  like  James'— similia. 

Therefore  the  colors  of  John's  and 
James'  hair  are  similia. 


2d. 

This  marble  is  not  that  one— hetera, 
The  other  is  uot  this  one— hetera, 
Therefore,  the  other  one  and  that 
one  are  hetera. 


5th. 
Loaf  sugar  is  sweet— homon. 
This  loaf  is  not  that  apple— hetera 
Therefore,  the  taste  of  sweet  in  this 

sugar,  and  the  taste  of  that  apple  are 

helera. 


4th. 
An  apple  is  not  a  peach- differentia. 
A  pear  is  not  an  apple— differentia, 
Therefore  a  pear  and  a  peacn  are  dif- 
ferentia or  similia. 


Gth. 
Sugar  is  sweet- homon. 
This  bread  tastes  like  sugar— similia, 
Therefore  the  taste  of  this  bread  and 
sweet  are  similia. 


78 


»^ 


7th. 
Sugar  is  sweet — homon, 
Vinegar  is  not  sweet — differentia, 
Therefore  the  tastes  of  sugar  and  of 
vinegar  are  differentia. 


8th. 
This  biscuit  is  not  that  one— hetera, 
This  biscuit  is  sweet— homon, 
Therefore  the  sweet  of  this  biscuit 
and  the  taste  of  that  one  are  hetera. 


9th. 
This  apple  is  not  that  one— hetera, 
This  pear  tastes  like  that  apple— sim. 
Therefore  the  tastes  of  this  apple  and 
this  pear  are  similia,  or  differentia. 


11th. 

This  cake  tastes  like  sugar— similia, 
Sue:ar  is  sweet — homon, 
Therefore  the  sweet  in  sugar  and  the 
taste  of  this  cake  are  similia. 


10th. 
This  apple  is  not  that  one— hetera, 
This  pear  does  not  taste  like  that  apple 

— differentia, 
Therefore  the  tastes  of  this  apple  aiid 
of  THIS  pear  are  differentia  or  similia. 


13th. 
The  color  of  the  barn  is  like  that  of 

the  house— similia, 
The  color  of  the  stable  is  not  like  that 

of  the  house — differentia, 
Therefore  the  colors  of  the  barn  and 

stable  are  differentia. 


12th. 
The  color  of  the  barn  is  like  that  of 

the  house— similia, 
John's  barn  is  not  the  barn  spoken  of 

— hetera, 
Therefore  the  colors  of  John's   barn 
and  of  the  house  are  similia  or  diff. 


15th. 
This  cake  Is  not  sweet — differentia, 
This  bread  is  not  the  cake — hetera, 
Therefore,  the  taste  of  this  bread  and 
sweet  are  differentia  or  similia. 


14th. 
Sweet  is  not  sour — differentia, 
8ugar  is  sweet — homon. 
Therefore  the  taste  of  sugar  and  sour 
are  differentia. 


16th. 
This  cake  is  not  sweet— differentia, 
This  bread  tasies  like  the  cake — sim. 
Therefore  the  taste  of  this  bread  and 
sweet  are  differentia. 


Now  from  the  foregoin/r  paradigms,  we  see  that  like  numbered  modes 
in  each  figure  give  like  results  in  the  conclusion  and   that  in  each  figure  we 
obtain  eleven  categorical  and  five  disjunctive  conclusions.    From  homoni- 
eal  premises  (1)  we  obtain  similia  in  the  conclusion;  from  heterical  premises 
(2)  hetera;  from  similical  premises  (3)  similia;  from  differentia  premises   (4) 
differentia  or  similia ;  from  homo-heterical  premises  (15  and  8)  hetera;  from 
homo-similical  premises  (16  and  11)  similia;  fiom  homo-differentia  premi- 
ses (7  aad  14)  ilifferentia;  from  similo-heterical  premises  (9  and  12)  simi- 
lia or  differentia;  from  similo  difierential  premises  (13  and  16)  differentia; 
and  from  heterico  differential  premises  (10  and  15)  differentia  or  similia;  in 
all  clearer  categorical  and  fine  disjunctive  conclusions.    And  of  the  catego- 
rical conclusions,  four  are  similia,  three  are  hetera  and  four  are  differentia. 
Now  the  foregoing  figures  with  their  modes  exhaust  the  power  of  syllogising 
with  the  first  four  kinds  of  propositions,  in  the  singular  syllogism. 


79 

But  the  fifth  and  sixth  classes  of  propositions  may  be  combined  with 
homonical  and  heterical  propositions,  in  figures  and  modes  similar  to  those 
already  exhibited.  And  letting  A  stand  for  the  middle  term,  as  before,  the 
following  paradigm  will  show  the  combinations  in  the  first  figure.  And 
with  the  fifth  and  sixth  classes  of  propositions  we  may  use  the  sign  —  equal 
to,  between  commensura,  and  >  or  <  the  sign  in  commensura,  just  as  in 
mathematics. 


1st. 

A  &  B  are  homon, 
C  &  A'  are  homon, 
/.  G=B. 


i  2d. 

A  &  6  are  hetera, 
C  &  A  are  hetera, 
.*.  C  &  B  are  hetera. 


84. 


A=B, 
C=A, 
.-.  0=B. 


A>B 

C>A 

.•.C>B 


I    A<B 

'    C<A 

.•.C<B 


4th. 

A<Bor  A>B 

C>Aor  C<A 
.•.C=BorC<BorC>B 


5th. 
A  and  B  are  homon, 
C  and  A  are  hetera 
'.C  and  B  are  hetera. 


6th. 

A  and  B  are  homon 
C=A 
•.C=B. 


7th  i 

A  and  B,  are  homon, 
C<A,  :orC>A 
.•.C<B   :.-.C>B. 


8th. 

A  and  B  are  hetera, 
C  and  A  are  homon, 
.C  and  B  are  hetera. 


9th. 

A  and  B  are  heterft, 
C=A 
.•.C=BorC<BorC>B. 


10th. 
A  and  B  are  hetera, 
C>A  I  orC<A, 
.C=B,  orOB,  or  C<B, 


12th. 
A=B. 

C  and  A  are  hetera, 
.C=B,  or  C<B,  orOB. 


nth. 
A=B, 

C  and  A  are  homon, 
,\C=B, 

13th. 
A=l, 

C<A,  ;  or  C>A, 
.•.C<B,  ;  .-.OB. 


14th. 

A>B,  orA<B, 
0  and  A  are  homon, 
.•.C>B    :  .•.C<B, 


15th. 

A>B  ;or  A<B, 
C  and  A  are  hetera, 
.•.C=B,  or  C<B,  or  C>B. 


16th. 

A>B  orA<B, 

C=A    !    C=A, 

.•.U>B    :    C<jB. 


We  do  not  deem  it  necessary  to  give  paradigms  of  the  modes  of  the 
remaining  three  figures  in  which  homonical,  heterical,  commensural  and  in- 


^    k 


80 

commensural  propositions  arc  combined.  Now  the  four  figures  with  their 
modes,  in  which  the  first  four  classes  of  propositi Dns  are  combined  and  the 
four  figures  with  their  modes,  in  which  homonical  heterical,  commensural 
and  incommensural  propositions  are  combined,  exhaust  the  whole  power  of 
syllogising  in  singular  syllogisms,  i.  e.^in  comparing  two  existences  by  the 
means  of  an  homanical  existence  or.  of  two  similical  or  commensural  exis- 
tences. We  hove  not  put  the  words— all,  every,  no  &c.,  before  any  of  the 
terms,  because  these  words,  as  we  have  heretofore  shown,  do  not  change  the 
character  of  the  affirmation,  but  belonging  to  the  terms  liiey  are  used  to  dis- 
tinguish and  characterise  the  existence,  whicli  we  are  comparing,  and  they 
may  be  thrown  out  of  every  proposition,  in  which  they  occur,  excepting 
numerically  complex  propositions,  by  changing  the  wording  of  the  proposi- 
tion and  without  affecting  the  result;  as  all  men  are  mortal,  is  equivalent  to 
man  is  mortal,  i.  e.,  one  of  the  gregaria  sine  qua  non  of  man  and  mortality 
are  homon.  The  propositions,  All  the  Apostles  were  Jews;  All  the  boys  in 
the  room  are  barefooted,  &c.,  are  numericall}'  complex  propositions,  and  they 
are  not  used  in  the  singular  syllo^jism  The  words— some,  most,  a  few,  *fcc., 
also  distinguish  merely  the  numerical  relations  inter  similia  upon  a  certain 
generalization.  And  by  the  custom  of  our  language,  every  proposition,  in 
which  they  occur,  may  be  stated  in  other  words,  which  shall  not  express,  but 
imply  their  substance;  as  some  apples  are  sour,  into  all  apples  are  not  sweet ; 
i.  e.,  sweet  and  sour  are  not  gregaria  sine  qua  non  of  apples.  And  hence, 
SOME,  MOST,  a  few,  &c.,  show,  in  propositions,  an  indefinite  numerical  rela- 
tion among  apples,  for  instance,  which  as  apples  are  similia,  but  which, 
outside  and  over  and  above  the  gregaria,  sine  quibus  non,  possess  other  gre- 
garia, which,  when  considered,  enables  us  to  distinguish  and  further 
difir«rentiatc. 

CHAPTER  XVIII. 

EXPLANATION  OF  THE  SYLLOGISM. 

If  a  man  were  in  a  wood  among  fallen  timber  and  found  two  logs, 
which  he  was  unable  to  lift,  and  whose  comparative  lengths  he  desired  to 
know,  without  the  use  of  the  syllogistic  process  he  would  not  be  able  to  ac- 
complish his  object.  If  however,  he  should  cut  a  rod,  which  we  will  call  A, 
he  could  go  with  it  to  the  first  log,  which  "xe  will  mark  1st,  and  find  that  1st 
and  A  are  commensura,  and  then  with  his  rod  he  could  go  to  tfle  second  log, 
which  we  will  mark  2d,  and  find  that  2d  and  A  are  commensura  and  then  he 
would  have  the  premises  of  a  syllogism :  1st  and  A  are  commensura,  2nd 
and  A  are  commensura,  therefore  1st  and  2d  arc  commensura ;  or  lst= A,  2>  A, 
if  it  be  so  and  therefore  2d^  1st.  And  without  the  power  to  syllogise  the  car- 
penter could  make  no  use  of  his  foot-rule,  the  shoemaker  no  use  of  his  last,  the 


81 
farmer  no  use  of  his  half-bushel ;  no  one  could  put  into  a  pile  one  cord  of  wood ; 
and  no  one;  could  tell  without  first  having  knocked  his  hat  oft'.whether  the  door 
in  his  house  was  high  enough  to  let  him  enter  without  bending  his  body.  The 
process  of  syllogising  is  used  by  every  person  in  the  daily  vocations  of  life, 
and  it  always  has  been  so  used  from  the  creation  of  man. 

But  notwithstanding  the  almost  constant  use  of  the  syllogism  by  all 
men,  the  process  itself  has  been  misunderstood  both  by  the  friends  and  the 
encmies_of  logic.  The  opposers  of  logic  have  represcnied  that  if  the  syllo- 
gism be  a  true  process  of  reasoning  u  cd  by  us  in  matters  about  which  we 
reason,  men  could  not  have  reasoned  at  all  before  the  time  of  Aristotle,  who 
is  regarded  as  Die  true  expounder  of  logic;  which  is  argument  is  analogous 
to  the  lollowing;  If  the  wheels  of  a  wagon  turn  upon  the  principles  of  the 
lever  before  these  principles  were  understood  men  could  not  have  driven 
wagons.  The  contempl,  ht>wever,  which  the  oj.noseis  have  heaped  upon 
logic,  and  of  which  its  innnds  complain,  is  not  owing  to  the  want  of  a  syllo- 
gistic process  in  the  mind,  but  to  the  circumstance  that  the  friends  of  logic 
have  been  neither  able  to  explain  this  process,  nor  to  refute  the  objections  of 
its  advisaries. 

For  the  explaination  of  the  syllogism,  most  of  the  writers  upon   logic 
have  relied  upon  the  Aristotlean  dictum  de  omne  et  nullo— what  ever  can  be 
predicted  of  a  class  can  be  predicted  of   any  individual   of   that   class— and 
Jieuce  tiiey  say  that  the  middle  teim  must  always  be  distributed  in  one  of  th« 
premises  by  being  the  subject  of  a  universal  affirmative  or  the  predicate  of  a 
negative  pn^prosilion,  which  in  our  opinion  amounts  to  nothing  so  far  as  the 
syllogistic  process  itself   is  concerned.    For   a   class  is  nothing  else   than 
several  individuals  inter  se  similia,  or  but  one  individual  difl^erentiated   from 
nil  other  things;  and  hence  the  dictum  asserts  merely  that  whatever  can   be 
predicated  of  each  one  of  similia  can  be  predicated  of   any  one  of   similia; 
and  although  this  is  true,  it  is  but  a  part  of  the  whole  truth.    If  we  have  be- 
fore us  several  marbles,  the  colors  of  which  are  inter  se  similia,  we  may  with 
equal  truth,  turn  the  dictum   th3  other  way,  and  say   that  whatever   can  be 
predicated  of  the  color  ot    any  one  of   the  class,  can  be  predicated   of   the 
color  of  each  op.c  of   the  class,  for  the  reason  that  the  colors  are  inter  se 
similia.    And  for  the  same  reason  and  for  none  other,  to-wit,  that  the  indi- 
viduals are  similia   in  the  respect  in  which  every  one  or  any  one  is  spoken 
of,  or  joined  with  a  certain  predicate  in  a  proposition,  does  the  dictum  mean 
anything:  that  there  actually  are  in  nature  similia,  difterentia,  commensura 
and  incommensura,  is  the  foundation  of  the  dictum,  and  yet  a  syllogism  may 
be  constructed  of  homonical  or   heterical   premises.    And   from  the  notion 
Ihat  in  every  syllogism  tha  middle  term  must  be  be  distributed  in  one  of  the 
premises,  i.  e.,  stand  for  a  whole  class  of  individuals  eo  nomine  et  innumero; 
while  in  truth  it  is  never  does  so  stand,  but  always  rcprestiuts  an  homonical 


83 
individual,  or  an  individual  of  similia,  or  of  commensura,  the  friends  of  logic 
have  been  overpowered  by  their  own  logic.  And  hence  the  friends  of  logic 
have  conceeded  to  its  adversaries,  that  in  every  legitimate  syllogism,  the  con- 
clusion contains  nothing  which  is  not  emplyed  and  virtually  asseited  in  the 
premises.  For  say  they  we  reason  from  generals  to  particulars,  and  what  is 
trje  in  general  is  true  in  particular — dictum  deomni  et  nullo.  And  although 
J.  Stuart  Mill  was  able  to  see  that  Aristotle's  dictum  was  only  adapted  "to  ex- 
plain in  a  circuitous  and  paraphrastic  manner  the  meaning  of  the  w^ord 
class."  Yet  he  too  along  with  the  rest  was  overpowered  by  the  dictum. 
And  hence  he  says  "It  must  be  granted  ihat  in  every  syllogism  considered  as 
an  argument  to  prove  the  conclusion,  there  is  a  petilio  princlpii.  W  aen  we 
say  all  men  are  mortal,  Socrates  is  a  man,  therefore  Socrates  is  mortal,  it  is 
unanswerably  urged  by  the  adversaries  of  the  syllogistic  theory,  that  the 
proposition,  Socrates  is  mortal,  is  presupposed  in  the  more  general  assump- 
tion, all  men  are  mortal ;  that  we  could  not  be  assured  of  the  mortality  of  all 
men,  unless  we  were  previously  certain  of  the  mortality  of  every  individual 
man;  that  if  it  be  still  doubtful  whether  Socratee,  or  any  other  individual 
you  choose  to  name,  be  mortal  or  not,  the  same  degree  of  uncertainty  must 
hang  over  the  assertion,  All  men  are  mortal;  that  the  general  principle,  in- 
stead of  being  given  as  evidence  of  the  particular  case,  can  not  itself  be 
taken  for  true  without  exception,  until  every  shadow  of  doubt  which  could 
affect  any  case  comprised  with  it  is  dispelled  by  evidence  aliunde  and  then 
what  remains  tor  the  syllogism  to  prove  ?  That  in  short,  no  reasoning  from 
generals  to  particulars  can,  as  such,  prove  any  thing;  since  from  a  general 
principle  you  can  not  infer  any  particulars  but  those  which  the  principle 
itself  assumes  as  foreknown.    This  doctrine  is  irrefragable." 

Now  this  "irrefragable  doctrine"  is  owing  to  a  misconception  of  the 
nature  of  propositions  and  of  their  combinations  in  the  syllogism.  In  the 
first  place  it  is  not  true,  although  it  has  generally  been  conceeded  to  be  so, 
that  there  is  nothing  contained  in  the  conclusion,  which  is  not  implyed  in 
the  premises.  In  the  syllogism,  A  and  B  are  similia,  C  and  B  are  similia, 
therefore  C  and  A  are  timilia,  we  have  indeed  the  existences  A  and  C  in  the 
premises,  their  relation,  however,  to  each  other,  is  neither  expressed  nor  im- 
plyed in  either  of  the  premises,  but  it  is  evolved  from  the  combination  of 
the  premises.  And  if  it  bo  meant  that  by  the  combination  of  the  premises 
the  conclusion  is  implicated,  this  indeed  is  true,  but  this  certainly  can  not  be 
urged  as  an  objection,  for  it  is  of  itself  an  approval  of  such  combination  for 
the  purpose  of  gaining  a  result,  which  we  can  not  obtain  without  such 
combination.  In  order  to  understand  this  matter  clearly,  it  is  necessary  that 
we  enter  into  an  elaborate  explanation  of  the  syllogism.  We  have  shown 
heretofore  that  when  the  existences  really  compared  in  any  proposition  are 
clearly  set  out  by  the  wording  of  such  proposition,  the  ttrms  of  the  proposi- 


8a 

tion  may  be  ♦ransposed ;  as  all  men  are  mortal,  i.  e.,  ono  of  the  gregaria  sine 
qua  non  of  man  and  mortality  are  homon,  and  by  transposition,  mortality 
and  one  of  the  gregaria  sint  qua  non  of  man  are  homoa.  And  hence  when 
a  proposition  is  so  worded  that  the  terms  may  be  transposed  (and  every  pro- 
position can  and  ought  to  be  so  worded  when  it  is  considered  in  a  scientific 
view)  it  may  be  combined  with  another  proposition  worded  in  like  manner, 
in  any  one  of  the  four  figures ;  and  therefore,  an  explanation  of  the  syllogism 
in  any  one  of  the  sixteen  modes  of  any  figure,  will  be  an  explanation  of  the 
like  numbered  modes  in  aU  the  figures. 

V\e  will  commence  our  examination,  therefore,  with  mode  1st  in  iho 
paradigms  in  which  the  first  four  kinds  of  propositions  were  used.  Take  the 
syllogism.  All  snow  is  white  or  snow  is  white.  The  foam  of  the  sea  is  white, 
therefore  the  colors  of  enow  and  of  the  foam  of  the  sea  are  similia, 
i.  e.,  snow  and  the  foam  of  the  sea  are  similia  in  one  facial  gre- 
garium— color— which  facial  gregarium  of  snow  and  that  of  the  foam 
of  the  sea^  have  each  of  them  been  differentiated  from  tho  other  four 
nominal  truths  into  color;  but  inter  se  they  could  not  be  differentiated,  and 
therefore  they  are  similia.  But  we  have  heretofore  shown  that  fcetera  lis  at 
the  very  foundation  of  our  knowledge.  Suppose  then  that  we  look  at  the 
color  of  paper,  and  without  any  reference  to  discrimination  say— this  is— 
and  having  turned  our  eyes  away  from  it,  look  at  the  same  paper  again  and 
say- this  is;  now  is  this  the  thing  which,  we  have  said,  is,  when  considered 
as  grounded  in  the  ego,  the  same  thing  in  both  cases?  certainly  not;  and  why 
not?  Simply  for  the  reason  that  their  times  can  be  heterated,  and  the  power 
of  our  minds  to  heterate,  gives  us  the  knowledge  that  then  and  now  are 
hctera  and  that  an  existence  grounded  in  the  ego  five  minutes  ago  is  not  sub- 
jectively the  same  existance  grounded  in  the  ego  now.  But  if  two  existences 
can  be  heterated  only,  the  two  must  be  to  us  inter  se  similia;  and  therefore 
when  we  have  said,  this  is,  and  that  is,  if  we  can  discriminate  no  farther 
we  must  say,  this  and  that  are  similia,  and  merge  the  two  homonical  propo- 
sitions into  one  similical  proposition.  Returning  therefore  to  the  premises. 
Snow  is  white.  The  foam  of  the  sea  is  wbite,  the  heterical  whitks  are  similia 
we  can  discriminate  them  no  farther  than  into  hetera,  and  hence  the  conclu- 
sion must  follow  that  the  color  of  snow  and  that  of  the  foam  of  the  sea  are 
similia.  But  when  we  say.  Snow  is  white.  The  foam  of  the  sea  is  white, 
therefore  the  colors  of  snow  and  of  the  foam  of  the  sea  are  similia,  we  must 
recollect  that  the  hetericai  whites,  which  are  subjectively  similia,  have, 
each  of  them,  an  objective  where,  and  therefore  they  are  also  objectively 
similia,  while  if  we  should  project  them  into  an  homonical  where,  they 
would  be  objectively  homon.  The  above  premises,  therefore,  contain  four 
subjective  existences,  two  of  which  the  heterated  whites,  are  subjectively  and 
objectively  similia;  objectively  however,  there  aie  but  two  existences  in  the 


84 

premises  to  wit,  the  color  of  snow  aud  the  color  of  the  foam  of  the  sea;  Mud 
objectively  the  s\'lIogism  in  mode  1st,  in  the  conclusion  locates  these  "objec- 
tive existences,  as  similia  in  their  respective  wiieues. 

Mode  2d,  if  we  consider  the  four  hetcrcical  existenoci  of  the  premises 
merely  subjectively,  they  would  not  bring  us  into  a  conclusion;  but  two  oi 
the  subjective  existances  must  be  considered  as  occupying  an  homonical 
where  in  an  homonical  time;  they  must  be  objectively  homon.  When  we 
say  1st  and  2d  are  hetcrn.  3d  and  2d  are  hetera,  therefore  1st  and  3d  are  hetera, 
the  two  subjective  2ds  must  be  referred  to  an  homonic:d  where  at  an  liomoui- 
cal  where  at  an  homonical  time;  but  Isl  and  3d,  cuiiiun  be  homon  for  they 
are  not  compared  with  each  other  In  either  of  the  premises,  Imt  they  are 
brought  together  by  means  of  2d,  and  if  2d  and  both  1st  and  3d,  be  hetera,  as 
stated  in  the  premises,  1st  and  3d  must  also  be  hetera.  It  may,  however,  be 
said  that  in  tiiis  mode  the  conclusion  does  not  follow  from  the  combination 
of  premises;  tor,  if  we  put  before  us  three  objective  existences,  marked  Isl 
2d  3d,  we  can  saj  tirst  is  not  tiiird,  without  comparing  each  of  these  with 
second.  This  is  true;  but  it  is  the  distinguishing  terms,  1st  aud  3d,  which 
enable  us  to  jump  the  middle  existence.  Suppose  we  apply  our  nose  to  a 
rose  and  say  This  (1st)  smell  is  not  that  scent,  we  then  apply  our  nose  again 
and  say,  This  (2d)  smell  is  not  the  1st  smell,  therefore  2d  smell  and  that  scent 
are  hetera.  In  this  case  the  1st  smell,  which  is  the  middhj  existence  appears 
twice  suhjectivol}^  but  we  refer  these  t v^  'Uyeciive  existences  to  au  homoui. 
cal  where  and  time,  aud  therefore  th.;>  ...o  homon,  and  without  this  middle 
existence  we  could  not  gain  the  conclusion,  that  second  smell,  and  that  l^L 
SCENT,  the  homonical  scent  menti(mcd  in  the  tirst  premise,  arc  hetera. 

In  mode  3d,  each  of  the  premises  is  a  conclusion  drawn  from  a  former 
syllogism:  as  A  is  white,  B  is  while,  tLerefore  the  colors  of  A  and  U  arc 
similia,  (mode  1st);  A  is  white,  C  is  white,  therefore  the  colors  of  A  aud  C 
are  similia  (mode  Ist);  and  from  these  conclusions  we  form  the  premises,  A 
and  B  are  similia,  C  and  A  are  similia,  and  hence  C  and  B  are  similia~con- 
clusion.     Mode  3d  needs  no  lurther  explanation. 

Mode  4th  is  somewhat  more  diflicult.  When  wc  say,  sweet  is  not  sour, 
bitter  is  not  sweet,  we  are  apt  to  look  back  at  the  words  sour  and  bitter,  and 
as  these  words  distinguish  dilierentia,  we  see  from  the  terms  that  sour  and 
BITTER  are  differentia,  and  hence  we  are  apt  to  infer  merely  difTerentia  from 
the  premises.  When  we  say,  A  peach  and  a  pccir  are  differentia  A  potato  aod 
a  pear  are  difieientia,  we  will  naturally  say,  A  potato  aud  a  peach  are  differ- 
entia, which-  indeed  is  true,  but  it  is  uotTHKUEFOUE  true,  it  does  not  follow 
from  the  premises.  Xo  categorical  concluaiou  can  he  legitimately  drawn 
frem  these  premises,  the  conclusi.m  which  really  does  follow,  is  that  a  potato 
and  a  peach  arc  cither  diflerentia  or  similia.  Tliis  will  easily  be  seen  if  we 
treat  a  peach  and  a  potato  merely  as  hetera  and  call  the  peach  first,  and  th« 


pota  o  second:  then  diBpiissing  from  our  m-ind  those  differential  names  'we 
say,  Ist  and  a  pear  are  differentia,  2d,  and  a  pear  .are  differentia  and  '^1;  do 
now  see  from  the  terms   Ist  and  2d  whether  they  be  diffe^mia  or  not    th« 
conclusion  follows  ligitimately in  our  m-inds  from  the  premTe    and  W  c<u 
elude  thaflst  and' 2d  are  differentia  or  similia.  ^'^"^'^^^^  '^"d  w*  c<m- 

T,w..  r'^?^'   "^""^  ^'^^^  modes,  whidi  are   in  substance  alike  are  easy 
T»>e  color  of  this  marble  is  white,  the  color  of  this  marble  and  Uie  coirof 
THATone  are  hetera,  therefore  the  color  of  that  one.  let  it  iTj^Trl" 
and  the  white  in  the  first  marble,  are  hetera..  Snow  is  white  snow  and  oJer 
are  hetera,  therefore  the  color  of  snow  and  the  color  of.  paper  ^"^^^^^^^^^ 

'  "^Thr 'tH^^'T.'  ''^"  '"  '  ^^^^^'  ^"^^  ^^-^-^  colors'areTetera       ' 

greater  difficuUie?    W,''""^  "'^^''^*  "  •"''  ""''  '''"^''''^  '^  '^^^'^^^^^  <^-tain 
thT^lnnt    r  ^     °    """'"^  this  apple  is  sweet,  that  pear  tastes    like 

f.i  Tr'  'f  '^""'  '''''  ''^"'  '^''  conclusion,  therefore,  that  pear  is  sweeU 
f^lows  fiom  the  premises,  though  this  conclusion  is  an  homonicTl  propos  1 
tion  The  taste  of  this  apple  and  sweet  are  homon,  the  taste  of  this  apl 
andtha  of  that  pear  are  similia,  therefore  the  .weet  in  the  apple  Ld^^^e 
e  .1^    -'  r''^'  similia;  but  similia  have  a  common  name,  and  therefi^ 

ion  t tt'ih     nr'"."'"  ''""'  '^  ^^"^'  '^^'^'-^^  -  -y  ^-  the  conct! 
8.on,lhHt  Uie  pear  is  sweet,  i.  e,.  that  the  taste   of   the  pear  and  sweet  are 

hon.oo.    Now  if  we  examine  the  above  syllogism  closely.'^.^e  wm  see  that  [n 

he  premises  there  are  subjectively  four  heterical  existences,  to  w  ^    t  Tl  " 

aste  of  this  apple;  ^nd.  Sweet;  3d,  The  taste  of  this  apple;  ;nd  4^^^  The  U  se 

of  n.at  pear;  three  ot    Which  subjective  existences  are   objectivel/homoo 

1  HE  TASTE  of  that  PEAR  only,  is  located  in  an  heterical  where  with  referTnce 

Z^^^^r^T'  '/  '*''!'"  '^'^  ''  '''''  apple,.sweet,  aud  the  tLe  of  thi 

Xectiv^er^r  f'-'"'^  '^"'^^^'^^'^  "'  ^^^  premises  subjectively;  but. 

bjectly   hese  three  are  homon.    But  the  swee.^. mentioned  in  the  concl^^on- 

ril  '"   -v  ''  ^Tr  ^'''  ^'^^  "^^  '^'''  '^  ''''  ^'''  P^«°^>«e.  tUey  are  ob- 
jectively snml.a,  and  because  they  are  similia  they  have  a  common  na^ 

and  wc  say  This  pear  is   sweet,  i.  e.,  one  of   the  gregaria  of   t^rpear  a^ 

son  one  of  these  similia  appears  ioeated  in  one  of  the  objective  wAeres 
iXrhtrj" '  "'  the  premises,  as  the  other  one  .f  the  similia  was  locZ 
m  the  ^ther  ^HERE  in  the  other  premise.     In  mode  first  we  saw  that  of  the" 

ZTiT::^''^'^^^^^  ''^^  -  the  firs,  premise  w  re 

11^;?!    V^^  ""'''  homon;  in  modes  ^h   and. 

nth  thb  tw6  subjective  existences  in  one  premise  and  one  of  the  SHbiective  ' 

exisences  in  the  other  premise,  are  objectively   homon.  .  Aad   we  ^uLt  sl^; 
e«r  J         r    ''  "^";'"^'^'!'  The  sweet  in,this  apple  and  .l-k,  ta^«  iothat 

pear  aie  s.miha;  and  dress  it  in  common  language,  viz:  That  pear  is  sweet, 


ii 


86 

«b4  then  combiDe  tbit  cooclution  witb  tbt  bmnoiical  proposition  {of  tbe 
aboTe  prtmises,  and  we  will  bt  in  mode  flrtt,  and  will  fi^ain  tbe  other  premise 
fit  the  abore  tyllof  ism  as  the  conclusion :  The  taste  of  this  apple  is  sweet  the 
taste  of  that  pear  is  sweet,  therefore  the  tastes  of  the  pear  and  apple  are 
•imilia.  And  to  make  the  matter  still  clearer,  we  may  suppose  three  persons 
whom  we  will  call  k,  B  and  C,  t9  be  sitting  in  a  room  with  two  apples  in  their 
hands.  A  tastes  both  of  the  apples  and  says  secretly  to  himself,  "this  apple 
is  sweet  and  that  apple  is  sweet,"  and  then  drawing  the  conclusion  in  mode 
Ist,  he  says  aloud,  '*this  apple  tastes  like  that  one;"  B  then  tastes  one  of  the 
apples  and  says,  **this  apple  is  sweet;"  well  then  says  C  from  what  A  and  B 
aay,  *^the  other  apple  is  sweet  also." 

But  hitherto  we  have  not  used  what  are  called  universal  propositions 
for  either  of  our  premises,  and  when  general  propositions  are  used  in  mede 
1st,  it  is  then,  that  a  petitio  principii  is  supposed  to  occur.  We  did  not  dis- 
cuss this  matter  when  treating  of  mode  1st,  for  the  reason,  that  we  desired 
t»  get  the  reader  further  along  in  the  knowledge  oi  some  of  the  other  modes* 
so  that  he  might  be  better  prepared  for  such  discussion.  When  we  say,  all 
men  are  mortal,  Socrates  is  a  man,  and,  therefore  Socrates  is  mortal,  it  is  said 
that  the  conclusion,  Socrates  is  mortal  is  implyed  in  the  first  premise.  All  men 
are  mortal.  The  difficulty  in  this  syllogism  is,  indeed  somewhat  below  the 
surface,  but  if  we  set  clearly  before  us  the  existences,  which  are  really  com- 
pared in  the  premises,  the  solution  will  be  more  easily  obtained.  All  men 
are  mortal,  or  iu  equivalent,  Han  is  mortal,  shows  that  one  of  the  capacial 
gregaria  sine  qua  non  of  man  and  mortality  are  homos;  Socrates  is  a  (one) 
Man,  shows  that  the  existence  called  Socrates  and  one  of  the  existences 
called  man  are  homon;  and  therefore  Socrates,  who  is  hom(»nical  witb  one 
man,  and  other  men  are  similia,  in  mode  1st.  The  simile,  mortality,  exisU  in 
every  object,  which  may  be  called  man,  but  Socrates,  I.  •.,  the  object  designa- 
ted by  that  name,  may  be  called  a  man,  and  therefore  this  simile  exisU  in  So- 
crates; for  MAN  is  the  common  name  of  similia.  In  the  foregoing  syllogism 
let  us  write  the  premises  and  conclusion  thus:  Socrates  and  ▲  man  are  ho- 
mon. One  of  the  gregaria  sine  qua  non  of  man  and  mortality  are  homon. 
Therefore  the  gregaria  sine  qua  non  of  man  and  the  gregaria  of  Socrates  are 
similia,  and  One  of  these  gregaria  of  Socrates  then  must  be  mortality,  Socrates 
must  be  mortal. 

Suppose  we  look  back  to  what  we  have  called  nominal  truths,  where 
we  saw  that  when  an  object  of  vision  arose  into  conciousness  we  called  it 
COLOR,  to  distinguish  it  from  conscious  truths  of  the  other  senses ;  and  sup- 
pose that  the  first  object  of  vision  should  have  been  the  color,  which  we  now 
call  red ;  red  then  would  have  been  called  color,  to  distinrilflh  it  from  con- 
scious tmths  sf  the  ether  senses.  Then  suppose  green  to  have  arisen  into 
consciousness,  green  too  would  have  been  called  soler,  to  distlnguisn  it  from 


87 
objects  of  the  other  senses,  and  then  red  and  green,  as  color,  as  distineuished 
from  objects  of  the  other  senses,  are  inter  se  similia,  and  therefore  each  of 
them  is  a  color.  Now,  if  we  collect  into  an  hemonical  proposlvion  the  rery 
thing,  which  enables  us  to  differentiate  objects  from  other  things  into  colors, 
to-wit,  visibility,  we  will  say.  All  colors  are  visible,  or  iU  equivalent.  Color  is 
visible,  i.  e..  Color  and  visibility  are  objectively  homon,  and  if  we  then  add 
That  red  is  a  color,  i.  e..  Red  and  one  color  are  homon,  it  will  follow  that  the 
object  called  red  and  visibility  are  similia  i.  e.,  red  as  au  object  distinguished 
from  conscious  truths  of  the  other  senses  is  distinguished  in  the  same  man- 
ner as  other  colors,  to-wit,  by  being  visible.  And  we  must  perceive  that  the 
first  premise  gives  visibility  as  the  ground  of  different Ution  from  the  con- 
scious troths  of  the  other  senses,  the  whole  of  which  ground  lies  partly  in 
the  visual  faculties  and  partly  in  external  objects,  that  is,  in  the  relation  of 
these,  and  it  gives  also  color  m  the  name  to  distinguish  that  part  of  the 
ground  lying  in  external  objecU;  and  hence  color  and  visibility  are  objective- 
ly homon.  The  second  premise  Ukes  one  of  the  subjective  similia  so  diff- 
erentiated, and  pronounces  this  similie  and  red,  a  color  further  distinguished 
among  colors  to  be  homon ;  and  hence  this  simile  and  any  other  simile  are 
similia  (non  simile  est  idem)  and  red  as  a  color  and  visibility,  when  located 
in  the  same  where,  are  homon,  for  similia  have  a  common  name  and  when 
their  wheres  are  homon ical,  they  are  objectively  homon. 

Again,  suppose  we  Uke  several  sticks,  each  one  of  which  we  dot  with 
differently  colored  dots  in  such  manner  that  by  looking  at  the  sticks  when 
thus  dotted,  we  cannot  by  the  dots  discriminate  one  stick  from  another,  and 
suppose  that  each  dot  on  any  stick  can  be  discriminated  from  any  one  of  the 
other  doU  one  the  same  stick,  and  to  distinguish  the  dots  inUr  se,  we  call 
one  A,  another  b,  c,  d,  Ac.    Now  letting  the  doU  in  the  aggregate  be  the  very 
things,  which  distinguish  the  sticks  before  us  from  other  things,  we  will  call 
these  dots,  in  the  aggregate,  in  fasceculo.  A.    But  supposing  that  by  the 
lengths  of  the  stieks  we  are  able  to  distin^ish  the  sticks  inter  se,  we  will 
call  a  particular  stick  B,  another  C  and  another  D.    Now  we  can  say  that 
one  of  the  dots  of  every  A  is  a,  I.  e.,  one  of  the  dote  of  any  A  and  a  are  ho- 
mon.   But  B,  this  particular  stick,  which  I  now  hold  in  my  hand  and  men- 
tion by  the  name  B,  is  a  (one)  thing,  whose  aggregate  dots  are  called  A.  i.  e. 
B  and  one  of  the  A's  are  homon,  therefore  any  one  of  the  A»s  excepting  the  ▲ 
which  I  hold  In  my  hand  and  mention  by  the  name   B,  and  the  A  which  I 
hold  In  may  hand  and  which  is  the  same  thing  as  B,  are  similia;  and  hence 
the  homonical  a  which  wo  find  in  any  A  excepting  the  A,  which  is  also  B 
has  a  simile,  a  dot  like  itself,  in  the  A  in  my  hand  which  I  may  call  also  B* 
B  is  A.  • 

It  must  be  confessed  that  the  exposition  of  this  matter  is  soms  what 
difficult;  and  heretofore  all  logicians  have  failed  to  understand  the  trite  state 


88 

cf  the  case,  but  by  tliinkin<r  over  the  matter  for  several  times,  we   hope  the 
,  reader^will  be  able  to^see  'ihrongh  it.    Perhaps  it  will  appear  more  clear  to 
-some  minds,  if  we  drsmiss  differential  terms  for  the  aggregate  existance.aud 
distinguish  them  merely  as  hetera;  then  one  of  the  gregaria  sine  qua  nonof 
l8t  object  and  mortality  are  homon ;  let  this  be  our  first  premise.    And  then 
:  It  must  appear  that  if  we  say  a  second  object  and  the  1st  are  similia,  it  will 
follow. ia  modi  6lh,  that  th©  simile  mortality  located  in  the  first  objects  has  a 
SIMII.E  located  in  the  second   one  and  this  simile   is  mortality.     But  if  after 
the  first  premise,  wu  say  tlmt  the  2d  objfect  is  one  of  the  first  kind  ot  objects 
Uiis:  proposition,   thongh  homonical,   is  quasi  similical,  and   the  conclusion 
.lrom.lhe  homonical  premises  that  the  gr'egarium  mortality  located  in 'the  1st 
object  has  a  simile  in  the  second  one  is  quite  evident,  and  this  simile  locaUed 
in  the^second  object  must  be  called  by  the  common  name,  mortality    and 
hence  one  of  the   gregaria  of  2d  object  and  mortality  arc  homon.    All'  men 
are  mortal,  \,  e ,  one -of  the  respects   in  which  men  are  similia  ana  mortality 
ve  .homon;.  Socrates  is  aman,  i.e.,  The  object  called  Socrates  and  one  of  the 
sjmilianamedman  are  homon;   therefore   ihe  respect,    to-wit,  mortality    in 
Tfhich.meo  aresimilinf  and  w4iich  is  a  grcgarium  in  other  men,  and  this  res- 
pect ha  the  object  catled  Soel'ates,  since  he  is  a  man— Socrates  is  mortal. 

The  reason  that  sylTogisua,  like  the  above  ai-e  so  diflicuU  to  understand, 
is-th«t  we  lose  sight  of  the  wheres  in   which  the  respects,   the  gre;;aria' 
which  render  objects  si miHa,' exist.    When  we  say.  Snow  is  white,  the  snovv 
tn  whrcirttiis  gregariunii  whIte,  exists,  or  did  exist,  has  or  had  an  objecUve 
WHiaiB;  bul  this  where  is  indefinfte  abd   undistiuguished  in  our  minds  from 
^ther  wheres.  '  BiJt  When  we  announce  td  a  friend  in  the  street  that  Snow  i;i 
White  and  then  add  that  an  object  in  our  house,  which  object  the  friend  nas 
neveisseenmw  heard  of  before,  is  snow,  he  will  immediately  conclude  that  the 
eolorsof  the  object  in  our  house  and  of  the  snow  located  in  an  indefinite  wuebe 
are  eimi4ia,.  and  therefore  he  would'say  that  the  object  in  our  house  is  white. 
.  Naw  we  do  net  <ioncede  that  this  argument  is  a  pelitio  principij,  that 
when  we  say  all  snow  is  white,  we-imply  that  the  object  in  the  house  is  white ; 
beftiT©  this  conclusion  can  be  reached,  without  seeing  the  object  itself,  we 
nni«t-Aist.lear<i  thit  the  object  in  the  house  and  snow  in  the  respect  of  color 
are  similia,  asd  thi^  we  do  when  we  arc  informed  that  the  object  in  the  house 
and  one  of  tlie^iciilia  named  snow  are  homon.    So  when  we  say  all   men 
arecaortal,  we  do  =not  imply  anything  respecting  the  object  named   Socrates 
for  Socrates  may  be- the  name  of  a  statue  of  of  a  fictitious  god  like  Jupeter' 
In  the^syllogism,   all  taen  aria  ihortal,  Socrates  is  a  man,  and  therefore  So-' 
cratesw.mortal,  however,  both  premises  us  they  are  usually  unnerstood  and 
the  coDclueion,  toe  false.     Iron  already  fused  Is  not  fusible  unless  it  he' first 
congealed  agam ;  neither  are  dead  men  mortal,  requiem  elernam  Domine  da  els 
--Ii^the  *illogi«n,  All  iiien  arc  mortal.  All  kings  are  mjEJO,  therefore  all 


89 
kings  are  mortal;  mortality  is  one  of  the  gregaria  sine  qua  non  of  man  and 
man  is  a  sine  qua  non  of  a  king,  and  therefore  mortality  is  a  sine  qua  non  of 
kmgs.  It  may  be  said,  indeed,  that  when  we  say  All  iron  is  fusible;  so  soon 
as  we  say  ef  any  object  that  it  is  iron,  we  have  alreadjr  in  the  first  premise 
asserted  that  it  is  fusible,  and  it  is  true  that  by  the  combination  of  the  prem- 
ises we  reach  the  conclusion :  and  this  is  the  case  in  every  syllogism,  whether 
either  of  the  premises  be  a  universal  proposition  or  not.  When  we  speak  of 
particular  objects  and  say  A  and  B  are  similia,  so  soon  as  we  say  A  and  C 
are  similia,  we  bring  B  and  C  to  be  similia,  yet  there  is  no  petitio  princiDii 
about  it.  *^ 

Now  when  we  say  Man  is  mortal,  we  mean  that  one  ef  the  gregaria 
sine  qua  non  of  man  and  mortality  are  homon:  but  when  we  say  Man  is  a 
mortal,  we  mean  that  each  man  and  one  of  the  similia,  each  one  of  which  is 
named  a  mortal  or  mortal  being,  are  homon:  and  this  proposition  brings 
man  among  the  similia  called  mortals,  in  each  one  of  which  there  exists  the 
SIMILE- mortality.  We  have  perhaps  gone  far  enough  with  the  explanation 
of  this  matter. 

Modes  7th  and  14th  are  very  easily  understood:  Sugar  is  sweet— 
homon;  No  vinegar  is  sweet,  or  Vinegar  is  not  sweet— differentia ;  There- 
fore the  tastes  of  sugar  and  vinegar  are  differentia.  The  9th  and  12th  modes 
are  easy:  and  after  having  gone  through  the  previous  explainations,  we  do 
not  deem  it  necessary  to  censider  the  remaining  modes,  as  the  principle  of 
each  of  them  has  already  been  exhibited  in  some  of  the  foregoing  explain- 
ations. It  may,  however,  be  well  enough,  in  order  that  the  reader  may  have 
a  clear  understanding  of  our  system,  to  take  a  view  of  those  rules  whick 
writers  generally  have  laid  down  for  the  regulation  of  the  syllogism. 

And  in  order  that  the  reader  may  better  understand  the  whole  matter, 
it  must  be  observed  that  logicians  have  divided  propositions  into  universal 
aftirmalive,  as  All  men  are  mortal,  which  class  of  propositions  they  distio-. 
guish  by  the  symbol  A;  universal  negative  marked  E,  as  No  gold  is  green; 
particular  affirmative  marked  I,  as  Some  islands  are  fertile;  and  particular 
negative  marked  O,  as  Some  men  are  not  black.  And  with  these  four  classes 
of  propositions  they  commence  to  syllogize  and  to  construct  rules  for  obtain- 
ing true  conclusions. 

And  the  first  rule  which  they  give,  is  that  Every  legitimate  syllogism 
must  have  three  and  only  three  terms— the  middle  and  the  two  terms  of  the 
conclusion.  Although  this  rule,  if  we  look  merely  at  terms,  be  true,  yet  we 
consider  logic  to  be  concerned  about  more  than  terms,  and  therefore,  we  state 
instead  of  this  rule  that  In  every  legitimate  syllogism,  there  must  be  four  and 
only  four  subjectively  heterical  existences  in  the  premises,  two  of  which— one 
m  each  premise— must  be  objectively  hetera,  and  the  two  of  which  with 
Which  the  other  two  are  each  compared,  must  be  objectively  homon.  or 
Simula  or  commensura  inter  se.  -  ^  » 


90 

The  second  rule  which  they  give,  is  that  Every  legitimate  syllogism   must 
have  three  aud  only  three  propositions:  in  this  we  are  agreed. 

The  third  rule  which  they  give,  is  Uiat  The  middle  term  must  not  be 
ambiguous.  This  danger  is  sufficiently  guarded  against  by  our  first  rule  re- 
specting everv  legitimate  syllogism. 

The  fourth  rule  which  they  give,  is  that  The  middle  term  must  be  dis- 
tributed once  at  least  in  the  premises  by  being  the  subject  of    an    universal 
affirmative  or  the  predicate  of   an  universal   negative   proposition.    For,  say 
they,  if  we  say  white  is  a  color,  black  is  a  color,  In   which  propositions  the 
middle  term— a  color— is  not  distributed,  we  will  conclude  falsly  that  black 
is  white.    But  after  what  we  have  said  heretofore,  we  think,  it  will   readily 
be  perceived  that  both  of  the  above  premises  are  homonical  propositions  aud 
that  the  predicates  ef  each— a  color— are  objectively  two  and  not  one  and  the 
same  existence,  they  are  not  liomon,  and  that  these  two  existences  have  been 
differentiated  from  existences  of  the  other  senses,  into  colors,  io  which  class 
of  existences  as  distinguished  from   other   things,  as  nominal   truths,  they 
are  similia,  the  name  color  will  distinguish  cither  of  them  from  existences  of 
the  other  senses.     When   therefore  we   say,  white  is  a  color,  black  is  a  color, 
it  does  not  toUow  that  white  is  black,  but  that   white  and    black   as  distin- 
guished, not  inter  se,  but  from  other  things  are  simUia.     White  is  a  color, 
black  is  A  COLOR,  therefore  white  and  black,  as  nominal  truths,  are  similia. 
But  it  does  not  follow  that  inter  se,  white  and  black  are  similia,  unless  it  &{>- 
pear  that  the  predicate,  a  color  in  the  first  premise,  and  the  predicate,  a 
COLOR  in  the  second  premise  are  inter  se  homon,  or  similia;  the  middle 
term  therefore  is  faulty,  not  because  it  is  not  distributed,  but  because  two 
existences  are  used  which  do  not   appear  to  be  inter  se  similia.    The  fourth 
rule,  therefore,  laid  down   by  writers,  as  a  guide  to  keep   us  upon  the  true 
process  of  the  mind  in  syllogising  correctly,  we  conceive  to  be,  not  only  of 
no  value,  but  erroneous. 

The  fifth  rule  given,  is  that  No  term  must  be  distributed  in  the  con- 
clusion, which  was  not  distributed  in  one  of  the  premises.  "All  quadru- 
peds are  animals,  a  bird  is  not  a  quadruped,  and  therefore  a  bird  is  not  an 
animal."  This  conclusion  is  evidently  erroneous;  and  it  is  quite  clear  that 
those,  who  were  engaged  in  the  constiuctioa  of  this  rule,  saw,  independently 
of  the  syllogistic  process  in  the  premises,  the  error  in  the  conclusion,  which 
from  the  appearance  of  the  words  in  the  premises  might  be  supposed  to  fol- 
low legitimately.  The  proposition,  "All  quadrupeds  are  animals."  means 
simply  that  each  quadruped  and  one  animal  are  homon,  and. when  we  add 
that  a  bird  is  not  a  quadruped,  i.  e.,  that  each  bird  and  any  quadruped  are 
differentia,  it  does  not  follow  that  each  bird  and  any  animal  «re  differentia^ 
what  fallows  legitimately,  is  that  each  bird  and  the  animals  homonical  or 
similical  with  the  animals  inaluded   in  the  predicate  of  the  homonical    pro- 


-  91 

position  "all  quadrupeds  arc  animals'*  are  differentia.    For  bird  and  animal 
are  brought  into  the  comparison  in  the  conclusion  by  means  of  an  homonical 
existence  or  similical  existences,  wi*h  which  they  were  each  of  them  com- 
pared in  the  premises.    We  stated  in  our  first  rule  that  each  existence,  which 
appears  in  the  conclusion,  must  be  compa'ed  in  the  premises  with  the  same 
middle  existence  or  with  two  existences   inter  se  simiMa  or    commcnsura. 
And  in  the  obove   premises   quadruped   is  compared   with  one   animal,  and 
quadrupeds  being  iater  se  similia,   bird  is  then  compared  with  one  of  these 
similia,  and  tlie  conclusion  must  be  that  the  animal  compared  in  the  homoni- 
cal proposition   and  found  to  be  one  of  the  quadrupeds  and  every  bird   must 
be  diffireutia,  but  nothing  can  be  infered  respecting  any  other  animal,  except 
it  be  a  simile,   than  the  animal   spoken  of  in  the  first   premise,   which  was 
homonical  with  quadruped,    lied    is  a  color.  Green  is  not  red,  are  premises 
ju^t  like  the  former,  aud  from  them    ',t  follows  that  the  on«  color   hemonical 
with  RED  and  green  are  diflerentia.     The   fifth  rule  ther.efore   is  of  no  value 
in  our  system,  it  is  erroneous  and  falacious  as  a  grade  in  the  syllogistic  process. 

The  sixth  rule  given,  is  that  From  negative  premises  you  can  infer 
nothing.  This  ru'e  in  our  system  has  no  meaning,  for,  we  do  not  admit  that 
there  is  any  such  thing  j»s  an  independent  negative  proposition.  But  calling 
such  piopositions,  which  have  no,  none  and  not  in  their  negative,  th# 
rule  itself  is  not  true,  it  is  o  ily  true  that  we  can  not  infer  a  categorical  con- 
clusion. From  the  premises  "A  fish  is  not  a  quadruped,  A  bird  is  not  a 
quadruped,"  it  legitimately  follows  that  a  fish  and  a  bird  are  differentia  or 
similia  (mode  4tb). 

The  seventh  rule  s:iven  is  that  if  one  piemise  be  n^igatiye  the  conclu- 
sion must  be  negative.     This  rule  in  our  system  means  nothing. 

Now  in  stating  every  homonical  proposition,  such  as  All  men  are  mor. 
ta),  we  must  be  careful  to  see  whither  the  predicate  be  one  of  the  gregaria  of 
the  subject  or  not;4"or  if  it  be  not,  and  it  be  represented  by  an  adjective  uame 
in  order  to  make  the  proposition  clear,  some  noun  must  be  placed  after  it,  or 
understood  for  adjective  names  which  are  not  the  representatives  of  grega- 
ria,  are  the  names  of  existences  standing  as  a  class  by  themselves.  When  w« 
say  "All  gold  ia  precious,"  we  mean  that  all  gold  and  one  of  the  things  es- 
teemed of  value  amon^  men,  are  homon ;  the  proposition  therefore  should  be 
slated  this;  All  gold  is  a  precious  thing,  and  then  we  can  add  that  All 
gold  is  a  mineral,  and  it  will  follow  that  the  mineral  homonical  with  gold  is 
a  precious  thing.  Mr.  Hamilton  gives  as  the  second  rule,  that  "The  subsump- 
tion  must  be  affirmative,"  and  he  illustrates  this  rule  by  the  following  ex- 
ample; "All  colors  are  phj^sical  phenomena,  no  sound  is  a  physical  phenome- 
na;" "Here"  says  he,  "the  negative  conclusion  is  false,  but  the  affirmative, 
which  would  be  true— all  sounds  are  physical  phenomena— can  not  be  in- 
ferred from  the  premises,  and  therefore  no  inference  is  competent  at  all." 


.') 


i, 


92 

(page  289 )  After  what  we  have  said  heretofore,  I  thick,  it  will  be  very  easy 
to  see  throufifh  Hamilton's  mistake.  When  we  say  that  "All  colors  are  physi. 
cal  phenomena,"  we  mean  that  each  color  is  a  (one)  physical  phenomenon 
and  when  we  add.  No  sound  is  a  color,  we  mean  that  any  sound  and  any  cobr 
are  differentia,  and  therefore  we  can  infer,  not  that  no  sound  is  a  physical 
phenomena,  but  that  all  physical  phenomena  homonical  with  colors  and 
sounds  are  differentia.  We  have  gone  far  enough  perhaps,  in  this  direction 
to  make  ourselves  understood  by  the  reader. 

Before  leaving  this  chapter,  however,   it  seems  necessary,   that  we 
should  make  some   remarks  tending  in   another  direction.    It  is  the  uni- 
mous  doctrine  of  logicians  hitherto,  tliat  one  of  the  premises  at  least  must  be 
what  they  call  a  universal   proposition,  otherwise  no  legitimatt  conclusion 
can  be  drawn.    And  hence,  if  we  should  take  a  stick  and  apply  it  to  a  table 
aid  find  the  lengths  of  the  stick  and  table  so  be  commensura,  and  then  apply 
the  stick  to  another  table  and  find  the  stick  to  be  longer  than  it,  and  we  should 
then  make  the  following  statement;  lsttable=stick,  2d  table<stick,  therefore 
1st  table>2d  table,  this  would  not  according  to  the  received  doctrine  be  a 
legitimate  syllogism.    But  if  this  be  not  a  legitimate  syllogism,  what  is  ii» 
General  propositions  are  necessary  at  all  to  enable  us  to  syllogise,  excepting 
3«^hen  we  wish  to  syllogise  with  gregaria  or  a  gregarium  sine  qua  non  of  ob- 
jects.   When  we  say  all  A  is  b,  i.  e.,  one  of  the  gregaria  sine  qua  non  of  A 
and  b  are  homon,  no  B  is  b,  i.  e.,  the  gregaria  sine  qua  non  of  B  and  b  are 
differentia,  it  follows  that  A  and  B  are  difterentia.    In  such  cases  as  these 
general  propositions  are  necessary;  but  such  cases  from  but  a  part  of  the  in- 
stances, in  which  the  syllogistic  process  is  used.    And  from  the  consideration 
no  doubt,  that  general  propositions  are  always  necessary  in  order  to  be  able 
to  syllogise,  J.  Stuart  Mill,  concluded   that  the  syllogistic  process  was  not 
realy  inferential  reasoning.    He  says  "In   the  above  observations   it  has  I 
think,  been  clearly  shown,  that,  although  there  i?  always  a^rocessof  reason- 
ing or  inference,  where  a  syllogism  is  used,  the  syllogism   Is  not  a  correct 
analysis  of  that  process  of  reasoning  or  inference;  which  is,  on  the  contrary 
(where  not  a  mere  inference  from  testimony)  an  inference  from  particulars  to 
particulars:  authorized  by  a  previous  inference  from  particulars  to  generals 
and  substantially  the  same  with  it;  of  the  nature,  therefore,  of  induction  " 
Now  when  we  tell  a  friend  that  the  heighth  of  a  stove  in  this  room  is  com 
mensural  with  the  heighth  of  a  stove  in  the  other  room,  which  latter  stove 
the  friend  has  never  seen,  and  thatithe  heighth  of  this  stove  is  three  feet  and 
then  ask  him  from  these  data  to  tell  us  the  heighth  of  the  stove  in  the  other 
room,  If  he  does  not  syllogise  and  on  the  syllogistic  process  make  an  infer- 
ence, I^houia  like  to  know  in  what  other  manner,  by  what  kind  of  induction, 
he  would  be  able  to  solve  the  problem. 


93 


CHAPTER,  XIX. 

EXPLANATION  OP   SYLLOGISM   CONTINUED. 

Having  explained  the  syllogism,  in  which  the  first  four  classes  of  pro- 
positions are  combined,  we  come  now  to  give  some  further  consideration  to 
the  syllogism   combining  the  first  and  second  and  fifth  and  sixth  classes  of 
propositions.    And  of  the  manner,  in  which  the  first  and   second   classes  of 
propositions  are  combined  in  the  syllogism,  we  have  already  said  suflScient; 
it  is  to  the  manner  of  combining  commensural  and  incommensural  proposi- 
tions, therefore,  that  we  will  more  especially  direct  the  attention  of  the  reader. 
In  our  explanation  of   propositions  heretofore,  we  observed  that,  similical 
and  differential  propositions  spring  from  homonical  propositions;  we  showed 
this  to  be  the  case  also  with  commensural  and  incommensural  propositions. 
Homon  is  at  the  bottom  of  all  propositions;  helera  are  at  the  bottom  of  all 
knowledge;  and  the  power  of  the  mini  t©  heterate  depends  upon  time  and 
space.    We  must  also  perceive  that,  homonical  propositions,  which  are  col- 
lected  into  heterical,  similical,  differential,  commendural  or  incommensural 
ones,  must  in  every  instance  have  a  local  reference  in  the  subject  or  predicate; 
for,  in  every  proposition  there   is  a  comparison  between  two  existences,  and 
if  these  two  existences  be  considered  merely  heterically,  they  can  not  sub- 
jectively be  homon;  to  be  Lomon  the  subjective  hetera  must  be  located  in  an 
homonical   where  at  an   homonical  time.    We  have  already  seen,   how  we 
come  to  have  the  knowledge  of  existence;  and  after  this  has  been  obtained, 
we  may  say  indeed,  that  this  grounded  in  the  ego  and  one  existence  grounded 
in  the  ego  are  homon;  but  when  the  one  existence  is  grounded  in  the  ego, 
it  is  located  there  in  the  same  where  with  this,  and  at  an  homonical   time; 
and  the  one  existence  and  the  this  refered  to  must  also,  irrespective  of  time 
and  space,  be  subjectively  similia,  otherwise  the  bringing  them   into  an   ho- 
monical where  at  an  homonical  time  will  not  make  them  homon.    An  object 
may  be  heard  by  the  ear  and  another  seen  by  the  eye;   irrespective  of  time 
and  space  they  are  differentia,  and  although  they  may  subjectively  be  located 
in  the  same  where  at  an  homonical  time   they  do  not  become  homon.     And 
where  we  say.  This  is  an  existence,  and  then  again.  That  is  an  existence,  the 
first  existance  and  the  second  one  are  hetera,  and  if  they  can  not  be  discrimi- 
nated further  they  are  similia.    Existences,  however,  is  a  name,  which  does 
not  distinguish  existences  inter  se.    But  if  we  say,  This  is  white,  and   then 
again,  That  is  white,  as  while  is  a  name,  which  distinguishes  existences  inter 
se,  if  the  first  ching  and  the  second  thing  be  not  similia,  in  the  respect  of 
color  the  word,  white  has  been  misapplied  to  one  or  both  of  ihem. 


94 

Kow  in  commensural  and  in  incommcnsuial  propositions,  the  things 
compared  are  always  similia,  yet  commensural  and  incommensiiral  propo- 
sitions are  not  derived  from  similia  but  from   homon.    If  we  take   a  cerlaiu 
stick  and  say,  the  length  of  this  stick  is  oke  (tlie  unit)  i.  e.,  the  length  of  thi," 
stick  and  ONE  are  homon,  and  we  then  go  to  an  other  stick  and  say    tl,c 
length  of  this  stick  and  one  arc  homon,  if  the  lengths  of  the  two  sticks  be 
not  commensura,  ONE  has  no  definite  meaning;  and   we  can  give  a  definite 
meaning  to  one  only  by  taking  some  homonical  thing  as"  the  unit  of  men 
urement.    If  then  w«  make  the  length  of  a  particular  stick  the  homonical 
thing  by  which  to  define  one,  and  apply  this  length  to  another  stick,  and  wc 
can  not  discriminate  the  lengths  of  the  two,  we  may  say,  the  length  of  ll,c 
first  stick,  the  homonical  thing  which  we  have  made  the  unit  of  measurc-- 
menl,  and  one  are  homon,  and  as  the  length  of  the  second  stick  when  com- 
pared with  the  first  cannot  be  discriminated  from  it,  we  must  from   a  mental 
necessity  call  it  ONE  also.    The  length  ol  the  first  stick  and  one  are  homon, 
the  length  of  first  stick  and  that  of  the  second  are  commensura,  therefore  the 
lengtu  of  second  stick  and  one  are  commensura;  but  commensura  must  «l 
necessity  have  a  commoa  name,  and  hence  the  length  of  second  stick  must 
be  called  one,  and  length   of  second  slick  when  not  compared  with  another 
and  one  are  homon.    And  if  we  combine  this  propo.silion,  with  the  homoni- 
cal one  which  gave  the  unit  of  measurement,  we  will  have  length  of  fiiNt 
stick  and  ONE  are  homon,   length  of  second  stick  and  one  are  homon,  there- 
fore engths.of  first  and  second  sticks  are  commensura,  since  one  and  one 
(not  wiceone)  are  commensura,  1=1;  and  hence  the  length  of  any  stick 
which  may  be  called  one,  will  be  commensural  with  the  first  stick.    If  how- 
ever, the  length  of  first  object<2d  and  2d<3d,  then  lst<3d,  and  we  ha.e 
hree  heterical  objects,  which  are  inter  se  incommeusura,  and  we  may  con- 

w  v^  ph"?  ^"r^^"'' """■"''"'"  !»'<•'"'.  l-ut  4th<5th.  therefore  lst<5tb, 
but  5  h<6th,  therefore  IsKCth,  ana  therefore  1st  or  any  of  one  of  the  objects 
after  1st,  is  less  than  6th,  and  so  on.    Here  then   we  have  six  objects  inter  so 
mcommensura  and  as  they  are  similia  in  kind,  each  of  them  in  a  like  man- 
ner has  been  diflerentiated  from  other  things,  and  they  have  a  common  name 
distinguishing  them  Irom  other  things  in  kind;  but  this  name  does  not  dis- 
tinguish Uiem  inter  se.    And  if  we  name  them  1st,  2d,  3d.  &c.,  these  distin- 
guishing terms  merely  distinguish  them  heterically  inter  se,  but  they  do  not 
show  the  incommensural   relations  existing  among  them,  and  therefore  by 
Uie  use  of  such  terms,  we  can  not  show  any  results  further  than   heterical, 
which  we  may  hare  obtained    by  comparing  those  objecU  inter  se.    There  is 
therefore  only  one  possible  way  for  us  to  form  a   language  by  whsse  terms 
we  may  be  able  to  show  the  results  of  the  minds  coutparisons  among  com ' 
mensura  and  incommensural  objects.    Alter  that  we  have  gained  the  knowl- 
edge of  the  homonical  thing,  which  we  establish,  as  .he  unit  of  measurement 


95 
in  an  homonical  proposition,  we  may  apply  this  homonical  unit  to  a  second 
object,  and  if  the  homonical  thing  be  measured  just  twice  upon  the  second 
object  we  may  arbitrarily  name  twice  one,  two,  and  tl^cn  twice  one  and  two 
will  always  be  in  our  minds  commensura,  and  two    will  show   the  resnit  of 
the  comparison  between  any  object  named  two,  and  the  homonical  thin- 
called  ONE.    And  by  naming  thrice  one,  TmiEE,  four  times  one,  four,  and  so 
on,  we  will  buf  e  the  cardinal  numbers  applied  to  similia.    One,  then  will  be 
a  common  name  for  all  objects,  which  are  inter  se  similia  and  inter  se  com- 
mensura; and  so  also  will  2,  3,  4,  &c.    But  1,  2,  3,  4,  &c.,  distinguish  incom- 
mensura  inter  se,  and  show  by  the  relations  of  the  homon  inter  hoteia    the 
incommensural  relations  existing  among  similia.    And  these  arbitrary  sign, 
ol  commensural  and  incommensural  relations  may  be  applied  to  any  similia 
in  nature,  by  taking  an  homonical  simile  as  the  unit  of  measurement;  they 
may  be  appi  led  to  lengths,  to  heats,  to  colds,  to  w-.-ights,  to  volumes  &c     It  is 
>he  peculiar  perogative  of   mathematics  to  develop  and   carry   out  these 
principles. 

But  we  must  see  that  the  unit  of  measurement,  in  all  cases,  is  the  pre- 
dicate of  an  homonical  proposition,  and  then  commence  commensural  and 
incommensural  propositions.    And  the  syllogism  with  commensural  and  in- 
c.mmensural  propositions,  is  used  in  every  branch  of  mathematics  from  the 
beginning  to  the  end.    And  as  the  demonstrations,  in  mathematics  depend 
upon  definitions,  it  is  necessary  to  consider  the  manner  in  wliioli  we  svllo- 
gise  upon  those  definitions.    We  have,  heretofore   said,  that  all  definirions 
whiQh  state  directly  what  a  thing  is,  are  contained  in  liom«nicaI  propositions  •' 
this  IS  the  case  id  mathematics,  and  as  geometry  affords  us  sufficient  illustra-^ 
tion  of  our  subject,  we  will  confine  our  remarks  to  it.    Geometry,  it  needs 
not  to  be  shown  here,  treats  of  relations  in  space,  and  hence  A  point  is  a 
position,  a  where  in  space,  i.  e.,  a  maihematical  point  and  a  where  in  ipace 
are  homon.    A  line  is  the  cause  of  consecutive  points  in  space.    A  strairht 
line  18  the  course  of  consecutive  points  in  a  uniform  direction  in  space  1% 
a  straight  line  and  a  course  of  consecutive  points  in  a  uniform  direction  in 
space  are  homon.    And  again,  the  portion  of  space  included  between  two 
lines  touching  each  other  at  a  given  point,  and  an  angle  are  homon.    Aniin 
the  portion  of  space,  which  being  included  by  two  straight  lines  touching  at 
a  given  point,  which  point  being  taken  as  a  center  and  a  circle  described   is 
a  quadrant  .f  the  circle,  and  a  right  angle  are  homon.  and  so  on.    All   the 
foregoing  definitions,  and  all  of  the  direct  definitions  upon  Which  in  geomAry 
demonstrations  are  constructed,  are  contained   in   homonical   propositions 
But  when  we  say,  an  acute  angle  is   an  angle  less  than  a  right  angle,  w.  do 
not  directly  define  an  acute  angle,  and  therefore  the  proposition  is  an  incom- 
mensural one,  and  so  also  when  we  say,  an  obtuse  angle   is  greater  Ui«ii  « 
right  angle.    And  it  must  be  observed  that  line  is  a  common  name  for  simi- 


-M««^. 


96 
lia  and  that  straight  line  is  also  a  common  name  for  similia,  line  being  a 
renus    ©f  wiiich  straight  line  is  a  species ;  and  so  also  with   angles  &c. 

But  atler  the  definitions  in   geometry,  then  lollow  what   arc  called    . 
axioms.    These  axioms  are  contained  in  commensural  and  in  incommensural 
propositions,  the  bottom  of  which,  as  we  have  seen,  is  homon.    But  the  com- 
mensural and  incommensural  propositions  which  contain  axioms  are  founded 
more  immediately  upon  the  syllogism.    The  axiom,  that.  Things  inter  se 
similia,*which  are  equal  to  the  same  thing  are  equal  to  each  other;  is  obvi- 
ously th«  condeasation  of  a  syllo^rism  into  a  commensural  proposition.    Let 
the  length  ol  a  cerUin  stick  be  the  homonical  unit  of  measurement  and  call 
this  length  one;  one  then  will  be  a  common  name  tor  all  lengths  commen- 
sural with  that  of  the  stick.    Now  if  we  apply  this  stick  to  another,  which 
we  will  call  A,  and  they  be  lound  to  be  commensura,  we  will  say,  A  and  1  are 
commensura,  A=l;  and  if  then  we  apply  the  first  stick  to  a  third  one  which 
we  will  call  B,  and  find  them  to  be  commensura,  we  will  say,  B  and   1  are 
commensura,  B=l;  then  we  have  the  syllogism  A=l,  B=l,  therefore  A==B. 
And  all   the  axioms  of   geometry  are   founded  immediately  upon  the   syllo- 
f  istic  process,  though  homon  is  at  the  bottom  of  the  whole  thing.    If  equals 
be  added  to  equals,  the  sums  will  be  equal,  is  very  plainly  founded   on   the 
syllegism.    If  A=B,  as  they  are  commensura,  we  may  call  each   of   them— 
three;  and  is  A'  =B',  as  they  are  commensura,  we  may  call  each  of   them— 
two;  then  if  we  apply  the  homonieal  unit  of  measurement  to  A,  we  find  that 
thrice  one  and  A  are  commensura  and  so  also  of    B ;  and  if   we   apply   the 
unit  to  A',  we  find  that  twice  one  and  A'  are  commensura  andjso^also  with 
B'  •  then  A-|-A'  must  be  equal   to  five  times  one,  or  five,  and  B-fB'=  five 
lim'es  one,  or  five;  and  we  have  the  syllogism,  A+A'  =5,  B-f  B'  =5,  therefore 
A+A'  =B-f-B' .    So  also  when  we  say  that  magnitudes,  which  being   applied 
to  each  other  coincide  throughout  their  whole  extent,  are  equal,  this  axiom  ii 
founded  upon  the  syllogism:  and  in  this  case  we  cojie  closer  to  the  homon 
at  the  bottom.    Suppose  wo  have  before  us  a  certain  object  called  A,  and  an- 
other called  B ;  if  now  we  represent  the  magnitude  of  A  by  A,  and  that  of 
B  by  B,  we  must  theh  say,  the  magnitude  of  A  and  a  are  homon,  and  the  mag- 
nitude of  B  and  b  are  homon;  but  it  a  and  b  cannot  be  discriminated  other- 
wise than  heterically,  if  they  coincide,  they  are  commensura,  a=b,  and  each 
of  them  may  be  called  d.  and   we  have  m.  of  A=d,  m.  of  B=d,  therefore  m. 
of  A=m.  of  B,    But  if  in  the  above  case  a  and  b  can  be  incommensurated, 
we  would  have  m.  of  A  and  a  are  homon,  m.  of  B  and  b  are  homon:  but  a<b 
therefore  m.  of  A  and  a  are  homon,  a<b,  therefore  m.  of  A<b;  but  m.  ol    B 
and  b  are  homon,  m.  of  A<b,  therefore  m.  of  A<m.  of  B,  which  is  the  foun- 
dation of  the  axiom,  that  The  whole  is  greater  than  unv  of   its  parts.    J?  or 
let  m  of  the  whole  De  represented  by  a,  and  the  m.  ot  any  part  be  represented 
by  b;  then  m.  of  the  whole  and  a  are  homon,  m  of  part  and  b  are  homon,  but 
b<a,  therefore  etc. 


97 

Now  it  may  be  said,  that  it  is  strange  that  axioms  which  are  regarded 
as  suflScient  truths  should  after  all,  be  arrived  at  by  a  process  so  diflacult  to 
understand.    This  however,  is  not  strange  at  all,  the  mind  rund  this  course, 
as  it  were,  in  a  flash  and  perceives  the  truths  expressed  by  axioms  without 
much  diflficulty;  though  to  trace   this  course  or  process  of  the  mind  is  very 
difficult.    There  are,  however,  some  of  the  elementary  truths  in  geometry, 
regarded  as  axioms,  which  seem,  at  first,  to  be  peculiar,  and  they  h^ve  been 
called  inductions;  they  are  contained  in  such  propositions  as  the  following; 
"Two  straight  lines,  which  have  two  points  In  common  cannot  afterwards 
diverge,"  "Two  straight  lines  cannot  inclose  a  space,"  "Two  straight  lines  in- 
tersecting each  other  cannot  both  ©f  them  be  parallel  to  a  third  straight  line," 
and  so  on ;  Such   propositions,  however  are  founded  upon  the   syllogism. 
Take  the  propesition.  Two  straight  lines  having  twopoints  ia  common  cannot 
afterwards  diverge,  or  what  is  equivalent.  Two  straight  lines  having  two  points^ 
in   common  must  coincide  throughout  their  whole  extent.    Now    a  mere 
glance  at  the  proi»osition  will  show  us  that  it  is  grammatically  in  the  poten- 
tial mode.    And  it  must  be  evident  that  there  are   differential  courses,   1.  e., 
that  a  straight  course  and   a  cw)oked  one  are  differentia,  and   that  two  lines 
one  of  which  runs  a  straight  course  and  the  other  a  cn>oked  one,  are  in  ca- 
pacity differentia;  given  a  certain  number  of  points  in  space,  a  line  that  can 
run  through  all  of  the  points,  and  a  line,  that  can  run  thi^ough  only  some  of 

them,  are  inter  se  differentia. 

8  ^  « 


B 


'» *■ 


Let,  therefore,  A  B  C,  be  a  straight  line  and  let  a  represent  its  uniform 
course  from  A  to  C;  then  a  straight  line  and  A  are  homon.  But  let  A  B  D 
be  another  line,  whose  course  from  A  to  D  is  represented  by  b,  then  A  B  D 
and  b  are  homon.  Then  if  a  and  b  be  homon,  or  similia,  ABC  and  A  B  D 
will  be  similia.  But  the  circumstance  that  the  point  at  D  in  b  can  be  dis- 
criminated from  any  point  in  the  C(mrse  a,  and  that  at  A  and  B,  a  and  b  co- 
incide, shows  that  the  courses  a  and  b  are  differentia.  Then  the  capacity  of 
thie  line  A  B  C,  and  a  are  homon,  and  the  capacity  of  the  line  A  B  D  and  b 
are  homon,  but  a  and  b  are  differentia;  therefore  we  have,  capacity  of  line  A 
B  C  and  A  are  homon,  a  and  b  arq  differentia,  therefore,  capacity  of  line  A  B 
C  and  B  are  difterentia;  but  capacity  of  line  ABD  and  b  are  homon,  capacity 
of  line  ABC  and  b  are  difterentia;  therefore  ABC  and  ABD  are  differentia;  A 
B  C  however,  by  hypothesis,  is  a  straight  line,  therefore  A  B  D  is  not  a 


98 

straight  line.  And  from  the  foregoing  demonstration,  we  can  easily  see*  how 
the  syllogism  underlies  the  proposition  tiiat  two  straight  lines  cannot  inclose 
a  space;  for,  a  space  inclosed  is  a  space  surrounded  by  consecutive  points, 
and  if  we  lay  down  one  straight  line,  another  straight  line  touching  the  first 
one  In  any  two  points,  cannot  diverge  from  it,  but  must  coincide  with  it  in  ita 
whole  course;  but  a  course,  a  mere  uniform  direction  can  inclose  nothing. 

"We  have  gone,  we  hope,  far  enough,  to  show  that  the  axioms  of  mathe- 
matics are  founded  upon  the  syllogism,  and  leaving  the  axioms,  therefore,  wc 
will  give  one  illustration  of  the  principles  of  our  system  of  reasoning  from  a 
simple  proposition  in  geometry.  Take  the  proposition  that  the  sum  of  the 
angles  of  a  triangle  are  eqial  to  two  right  angles. 


C 


B 


Let  DEC  be  tlie  triangle  and  prolong  the  side  DE  to  A;  and  from  the 
point  E  draw  EB  parallel  to  DC,  then  from  previous  syllogisms  we  know 
that  the  angles  CDE  and  BEAare  commensura;  we  also  that  the  angles  CEB 
and  DCE  are  commensura.  But  as  CDE  and  BEA  are  commensura,  we  may 
call  them  by  the  common  name  A;  and  as  CEB  and  DCE  are  commensura, 
we  may  call  them  by  the  common  name  B;  Then  either  CDE  or  AEB  is  an 
A,  and  either  CEB  or  DCE  is  a  B;  and  we  may  call  CED,  C;  then  AB 
and  C  and  the  sum  of  the  angles  of  the  triangle  are  commensura.  But  the 
sum  of  all  the  angles  that  can  be  formed  at  a  given  point  on  one  side  of  a 
straight  line  and  two  right  angles  are  commensura,  the  angles  A,  B  and  C  are 
the  sum  of  the  angles  so  formed  at  the  point  E,  therefore  A,  B  and  C  together, 
and  two  right  angles  are  commensura. 

CHAPTER  XX. 

ENTHYMEME,  SORITES  AND  DELEMMA. 

Having  explained  in  the  previous  chapters  the  manner  in  which  the 
syllogistic  process  proceeds,  wc  do  not  deem  it  necessary  to  elaborate  much 
upon  the  Entymeme,  Sorites  or  Delemma.  When  either  one  of  the  premises 
of  a  syllogism  is  expressed  and  the  other  understood,  the  expressed  premise 
with  the  conclusion  is  callen  an  entymeme;  as  Iron  will  rust,  therefore  the 
plowshare;  will  rust,  or  The  plowshare  is  iron,  and  therefore  it  will  rust.  In 
Bttch  cases,  it  is  easy  to  supply  the  premise,  which  is  understood.     Any  per- 


99 
son*  well  grounded  in  the  principles  of  the  syllogism,  will  have  no  difficulty 
in  managing  the  enthymeme. 

Now  when  a  conclusion  has  been  legitimately  drawn  from  premises, 
this  conclusion  may  be  made  a  premise  and  combined  with  either  of  the  for- 
mer premises,  and  another  conclusion  may  then  be  drawn;  and  then  this  lat- 
ter conclusion  may  be  combined  as  a  premise  with  the  first  and  so  on. 
When  we  continue  to  syllogize  in  this  manner,  the  chain  of  syllogisms  is 
called  a  Sdrites;  as,  A  and  B  are  similia,  B  and  C  are  similia,  therefore  A  and 
C  are  similia;  but  C  and  D  are  similia,  therefore  A  and  D  are  similia;  but 
D  and  E  are  similia,  etc.  And  this  process  may  be  pursued  with  any  of  the 
modes  and  figures,  which  we  have  given  in  the  preceding  paradigms. 
Thus:  A  and  B  are  similia,  B  and  C  are  difterentia,  therefore  A  and  C  are 
differentia;  but  C  and  D  are  similia,  therefore  A  and  D  are  differentia;  but 
D  and  E  are  differentia,  therefore  A  and  E  are  differentia  or  similia  etc. 
Now  we  stated  in  a  previous  chapter  that  there  are  five  objective  nominal 
truths,  and  If  we  lei  A  stand  for  one  of  them,  B  for  another  and  C,  D  and  E 
for  the  others  severally,  we  may  syllogize  upon  them  in  the  following  man- 
ner: A  and  B  are  hetera,  B  and  C  arc  hetera,  therefore  A  and  C  are  hetera; 
but  C  and  Dare  hetera,  therefore  A  and  D  are  hetera;  but  D  and  E  are 
hetera,  therefore  A  and  E  are  hetera;  and  therefore  A,  i.  e.,  the  thing  distin- 
guished by  the  name  A,  and  taste,  or  sound,  or  feeling,  or  color,  or  scent  are 
homon.  And  this  shows  us  the  manner  in  which  we  come  to  use  disjunctive 
propositions;  they  are  conclusions  of  syllogisms.  The  sky  is  either  clear  or 
cloudy,  why  ?  There  arc  two  states,  capacial  gregaria,  of  the  atmosphere, 
distinguishad  inter  se  by  the  names  clear  and  cloudy;  one  of  these  states  now 
exists,  therefore  it  is  either  clear  or  cloudy,  i.  e.,  the  present  state  of  the  at- 
mosphere and  either  clear  or  cloudy  are  homon.  And  when  we  say  that  Men 
are  either  black  or  white  or  ta^ny;  this  is  a  conclusional  proposition  drawn 
in  the  same  manner  as  the  one  above:  though  there  might  be  men  of  neither 
of  tuese  complexions,  for  aught  we  know.  And  in  the  conclusional  propo- 
sition just  given,  that  which  is  really  affirmed  is  that  one  of  the  facial  gre- 
garia of  every  man  and  on«  of  the  three  colors  a*mely,  black,  white  or 
tawny,  are  similia.  And  as  similia  have  the  same  name,  the  color  of  any 
man  and  black  or  white  or  tawny  are  houion.  Again:  Iron  and  glass  are 
hetera,  hetera  are  divided  into  two  classes,  namely,  similia  and  differentia, 
therefore  iron  and  glass  are  either  similia  or  differentia. 

Now  by  the  combination  of  dfsjunctive  cunclusional  propositions  in 
premises,  we  form  the  basis  of  what  is  called  the  Dilemma;  thus,  A  and 
either  B  or  C  are  similia,  i.  e.,  A  and  one  of  the  two  are  similia,  but  either  B 
or  C,  i.  e.,  either  one  of  them,  and  D  are  similia,  therefore  A  and  D  are 
similia,  therefore  A  and  D  are  similia.  And  it  must  be  noticed  that  there  is 
an  ambiguity  in  the  use  of  the  correllatives,  either,  or.  In  the  first  instance 


/ 


100 
A  and  either  Bor  C  are  siinilia,  we  mean  that  A  and  one  of  the  two  are^imi- 
lia,  while  A  and  the  other  may  be  differentia  for  aught  tnat  is  disclosed  by  the 
proposition ;  while  in  the  latter  instance,  either  B  or  C  and  D  are  similia,  we 
mean  that  Band  D  are  similia  and  also  that  C  and  D  are  similia.  And  it  is 
this  ambiguity  in  the  use  of  the  correllatives,  that  makes  the  dilemma  kind 
of  trap  by  which  men  are  caught  betore  they  are  aware  ol  it. 

Now  if  we  set  down  before  us  the  propositions,  A  and  either  B  or  C 
are  homon.  but  either  B  or  C  and  D  are  homon,  and  be  careful  not  to  be  mis- 
led by  .the  ambiguity  of  the  correllatives,  we  can  easily  see  by  censidering 
these  propositions  how  we  come  by  such  hypothetical  enthymcnes  as  the 
loUowing;  if  A  and  B  are  homon,  A  and  D  are  similia,  and  if  A  and  C  are 
liomon,  A  and  D  are  similia;  but  A  and  B  or  C  are  homon,  therefore  A  and 
D  are  similia;  (mode  Ist).  But  taking  again  the  two  disjunctive  propositions 
A  and  either  B  or  C  are  homon,  and  D  and  either  B  or  C  are  homon,  and  tak- 
ing'the  correllatives  in  both  instances  to  meam  one  ot  the  two  and  not  the 
otOier,  we  will  have  for  conclusion  that  A  and  D  are  either  similia  or  differen- 
tia, if  A  and  B  are  homon,  and  D  and  B  aie  homon,  A  and  D  will  be  simi- 
lia; and  if  A  and  C  are  homon,  and  D  and  C  are  homon,  A  and  D  will  be 
similia;  but  it  A  and  C  are  homon  and  D  and  B  are  homon  or  A  and  B  are 
homon  and  D  and  C  are  homon,  A  and  D  may  be  differentia.  Again ;  if  we 
take  the  propositions  A  and  either  B  or  C  are  similia;  E  and  neither  B  nor  C 
are  limilia,  it  will  follow  that  A  and  E  are  differentia. 

Now  it  i*  evident  that  we  may  take  any   categorical   proposition  and 
put  into  a  hypothetical  form.    Take  the  proposition,  Ice  is  cold,  and  we  may 
gay,  If  ice  is  cold;  but  from  this  latter  expression,  we  expect  some  conclusion 
©  follow,  and  we  state  the  proposition  in  this  hypothetical  manner   tor  the 
purpose  of  drawing  some  conclusion,   and  therefore  we   give  it.  this  illative 
wording.    And  in  such  cases  we  always  take  one  of  the  premises  of  a  syllo- 
gism and  sUte  it  hypothetical ly.    Take  the  syllogism,  Rainy  weather  is  wet 
weather,  it  IS  rainy  weather,  therefore  it  is  wet  weather;   now  we  may  state 
the  second  premise  hypothetically,  If  it  is  rainy  weather,  aed  draw  the  con- 
clusion, It  is  wet  wes^her,  leaving  the   first  premise   unexpressed.     We   call 
such  arguments  hypothetical  enthymemes ;   and  those  expressions  of  argu- 
ment which  have  been  commonly  called  hypothetical  syllogisms,  are  merely 
hypothetical  enthymemes  stated  first,  and  then  throwing  off  the  hypothesis, 
the  enthymeme  is  stated  again  categorically,  t©  show  that  the  conclusion 
does  not  only  follow  logically,  but  alao  that  the  premises,  from   which  the 
conclusion  is  drawn,  are  actual.    Thus  if  A  and  B  are  similia  then  A  and  C 
are  similia;  but  A  and  B  are  similia,  therefore  A  and  C  are  similia.    In  this 
example,  the  conclusion  introduced  by  thbkefore  does  Jiot  at  all  depend 
upon  the  expression,  if  A  and  B  are  similia,  then   A  and  C  are  similia,  but 
upon,  A  and  B  are  similia  and  another  premise  understood.    In  the  syllo- 


101 

gisnf,  A  and  B  are  similia,  (J  and  B  are  similia.  therefore  A  and  C  are  simi- 
lia, any  person,  who  looks  at  it,  und  grants  that  C  and  B  are  similia,  will 
readily  go  farther,  and  grant  that,  if  A  and  B  are  simtlia,  if  such  be  really 
the  case,  then  A  and  C  sre  similia,  and  when  you  convince  him  that  really  A 
and  B  are  similia,  the  hypothesis  is  thrown  oft',  and  be  acknowledges  that  A 
and  C  aiL'  .similia.  In  such  cases  the  conclusion  is  not  drawn  from  the  first 
hypothetical  eulhymeaic — if  A  und  B  are  similia  then  A  and  C  are  similia, 
but  from  A  and  B  are  similia  und  the  other  premise,  Band  C  are  similia,  «n- 
dersto.»d.  If  Socrates  is  virtuous,  thcji  he  merits  esteem;  but  Socrates  is 
virtuous,  therefore  lie  merits  esteem;  why?  The  viituoii>j  merit  esteem.  So- 
crates is  virtuous  tlierelore  he  merits  esteem.  We  do  not  consider  it  necessary 
to  go  into  an  elaborate  discussion  upon  such  mutter,  we  will,  however,  sub- 
join a  note. 

Note.— It  is  strange  that  neither  Arch' ishops  Whately  nor  Sir  Wm. 
Hamihou  were  able  lo  sound  to  the  bouom  of  what  they  call  hypothetical 
pr<»posilions,  nor  be  able  lo  perceive  the  true  nature  of  the  dilemma  "A 
hypotheiicHl  proposilion,"  says  Whaiely,  "ia  defined  to  be  two  or  more  catt^ 
troricals  united  by  a  copula  (or  conjunciion)  ami  the  different  kinds  of  hy- 
pothetical prjjpositious  are  named  fr»)m  their  respective  conjunctions:  viz; 
conditional  disjunctive,  causal  &3."  And  agrain;  ''A  conditional  proposition 
has  in  it  an  illative  foice,  i.  e.,  it  contains  two  and  only  two  categorical  pro- 
])ositious,  whereof  one  results  from  the  other  (or  lollows  froni  it)."  And 
a«.^ain,  "A  disjunctive  proposition  may  consist  of  any  membei  of  categwri- 
cals."  That  a  proposition  may  be  the  sutyect  of  another  prjposilion  is  very 
clear;  as  that  John  is  a  scholor,  is  not  denied;  but  (hat  one  proposition  ma}' 
be  a  dozen  propositions  is  certainly  very  strange.  Sir  Wm.  Hamilton  adopt- 
ing the  explanation  of  Krug  says(patj:e  108)  ''Alth(mgh,  llierefore,  an  hypothe- 
tical judgment  appear  double,  and  may.be  cut  into  two  different  judgments, 
it  is  nevertheless  not  a  composite  judgment.  For  it  is  realized  through  a 
simple  act  of  thought,  in  which  if  and  then,  the  antecedent  and  consequent 
are  thought  at  once  and  as  inseperable.  The  proposition  if  B  is,  then  A  is, 
is  tantamount  to  the  proposition,  A  is  through  B.  But  this  is  as  simple  an  act 
us  if  we  categorica!ly  judged  B  is  A,  that  is,  B  is  under  A.  Of  these  two, 
neither  the  one — If  the  sun  shines, — nor  the  other, — then  it  is  day — if 
thought  apart  from  the  other,  will  constitute  a  judgment,  but  only  the  tw'o  in 
conjunction."  Now  the  above  is  a  misconception  of  the  nature  of  proposi- 
tions, aj;d  it  arises  from  the  erroneous  noticms  entertained  by  Hamilttm  and 
others  respecting  predication.  Suppose  in  the  above  example  given,  we 
leave  the  if  and  then  out,  we  will  then  have,  the  sun  shines,  it  is  day:  Nmw 
Mr.  Hamilton  would  admit  that  here  are  two  propositions,  but  would  answer 
that  although  there  arc  two.  yet  it  is  not  shown  in  any  way  ihat  the  one  is 
connected  or  dependent  upon  the  other  without  the  words  ip  and  then. 
Very  well ;  take  the  propositions  A  is  B,  C  is  B,  A  is  C,  and  witliOUt  the  word 
tuekkfoke,  before  the  last  one,  it  is  not  shown  by  words,  that  this  is  the  con- 
clusion of  a  syllogism.  And  if  the  words  if  and  then  possess  the  magic 
•|)ower  to  merge  two  propositions  into  one,  we  may  use  them  also  to  merge  a 
syllogism  into  a  proposition,  thu«;  if  A  is  B  and  C  is  B  then  A  is  C,  which 
according  to  Mr.  Hamilton  would  be  merely  an  hypothetical  proposition. 
For  when  we  say  if  A   is  B  and  C   is  B,  we  expect  something  to   foUow  and 


102 
we  perceive  thai  A  is  C,  does  follovr,  and  hence  we  mav  iPimrd  .11 ..  : 

ilton's  erroneous  notions  of  what'hP  pu11«  .  «    1     ^,   *^  ^'!'^^^  ^     ^^-  ^'^^^ 
him  to  misunderstood  enthe^ whir  h^^^^^^         hypothetical    proposition    led 

page246,followinrEs:rr?Ha^i;J  :;L^tr'^^^^  ^>» 

position  invo  ve  onlv  the   ri.nnrri.t  »?  '     •  ^'/""^^^^ei,  an  hypothetical  pro- 

consequent,  it  til!  1?,1  ow  t^at'in;'l,ypmY,!ucal"'Jr'iir:'i"'  """  "'  "  ''"8'" 
more  ihan  tliree  but  of  1p««  Tltn.,    h..lL^!?     '.  ,        ^J^""Ki8'n  consists  not  of 

sense,  this  is  aclualh  the  case  O  ,  M.u*"'."'  "h"""''  *,""•  '"  »  'iK'-'on^ 
acnteness  have  viewed  t  le  livnotheMr,,  iln''  """'^'  '"'".^  ""gicians  of  great 
andoriwoproposiUons     Thi'iii      ?     ^^ 

Ld?-nrdr;iSSH^^^^ 

other;  if  one^be!  tl  SI^Ts  °s  XbJi  ,'„-     '-^^^  '""-" '"'  ""= 

the  other  hand,   he  ex  stance  orlnXl,"'"'^'^- ,  ^"  "'esubsumption,ou 

these  notions  comprisef?sexpresslv  it.'^fr''  "'."■'""."""  °''  '"«  "tlnr  of 
affirmed  or  expressly  denfedmHnlliMMvnfi  *"  •'  ","*  "f  '^'""^''P''  «^P>-i'8slv- 
different  significance  from  what  il„».  «l  "^'  "]  "'"  8"'>s"mptiou, a  whollv 
of  reality,  or  unreal iiva.ul  h.  lil  ''*P  ""'^  enounced  as  a  conditioli 

tion  left  untouched  nd  concerning  wr"""'  """  '"'""°  ^^""^  "'«  sub,ump- 
conclusion  declde^^  buins  a  c  "ar«1:ter  a  to.f.'iL'  ^  iV"'  '""'  ""'"""""'  '^"^ 
what  it  presented  in  theXrinnint  ••     Tht!  fvl?  '     itterent  m  the  end  from 
fromEsser.    And  hence  fror,h!„,,,!l''iL ''''P '*''*''""   Hamilton  obtained 
have  before  us  a  hat  and  a  b  o„m  fwWcI.  v,rT"'"''   "^  "''  .""PP""'  """  *-■ 
rate  existences)  and  wrsav  ifX  h«   u  „?,Th''?P''''''","  ''»P'>'«  •»"'  "^P"" 
are  separate  existences-  hut  the  1ml   L„?,.i^^'"""™'  ""^ ''""'"''  broom  are 
separate  existences?  we 'mKiumntion  to  ^'i,''';"'''"'  '""'='""=  "'"  '""  "f« 
and  this  third  term  Is  en^olved    be^fuse  t  re°,H™  .'."'".^  '■'"^"^!'  "'"•''  ""■"'■ 
eether  in  the  relation  of  lealou^nd  conseo"   'f "'   ,''  '»*  «""?""»  't^nd  to- 
they  are  asserted  to  be  reahties  and  HFvf ?«•!?>  fi  •'•j"."'*  subsumption  they 
sumption  we  take  the  sumo  Hon  to  he  «^>n»i      w     "■?  '"1"^  ""="  '"  "'«  ^''^ 
syllogising,  we  prove  thafthi  h.,  ;  "."k  ''°J  ""'•  "'"'  V  H'ie  method  of 

Ihesumptfon  Itha,,'nish1n^.U?  ""'  «"«  broom,  just  as  we  supposed  in 
ability  a^  Hamilton  should  have  bee^  T°"!  "■" TV,'-  ^""'"'"S  ""d  natural 
nonsenseof  the  German  In  wh!tH  u  m'"*^'"'  ""btle  and  trifling 
he  and  Whatley  are  also'in  the  dark  '^^'"1!'  '*""  D"e»'»«<ed  judgments, 
judgments  arefhose.  n  wh  ch  a  condign!'?"  "'^'*k<'"!  ^-^  "^>  "l>i'".matic 
in  the  predicate  and  as  th.if«  .nmh-  ."°  '» /"una,  both  in  the  subject  and 
disjunclire  form,  they  maV  also  a™ n'°"'?^  f  ?"  ''yPO'hetical  form  ind  of  a 
disjunctive.  If  x  is\  i7(x  ?s  eXr^R  l^'  be  denominated  Hypothetico- 
is  prohibited  eitherV  natiri  or  by'^poS.iJe'tr/"'"'  ".'"""^  Pi"'""''^"'  " 

e^t^r  I  o^rgSn"  t,rJt"x  I^MtT    '""'  "^    ^  ' <>  -  ""y  -  ' 
either  B  or  C  f  H.  and  thereh^e  x  is  ei  ..5r  k''  '^T^^'  "'?  P^''<^e»«-A  is 
errors  respecting  Dilemmati^  nrnnn.wl """":' ^  <""  C    Hamilton  carries  his    ' 

syllogismr;  bulle  w~t  irit^ZTrther. '"'°  """*'  ''^  *""'^  Dilemmatic 


108 
CHAPTEK  XXI. 

™E  StNOULAK  HO.V0XICAL  SVLIX)GISM. 

...orouSr  mr;^,;-''t;f  "sf  it;ir  ™  :f„  ^-^ :-'"'-"  -"^ 

for  us  to  show  the  further  apnl.cati.!  ,f  tiis  pro  es  ,.  Ihe'  "  '"'  ""'""" 
kuowledge.  We  have  already  shown  that  Irouftre'^'i^i^^r;!,"', wrr' 
mon.cal  propositions,  as  premise.,   we  may  caIn  «i„,il7»  ,?"  ^""" 

the  conclusion.    And  if  we  reoresont  „",i     ,  -r  commensura  in 

.vim       wu  lepieseut   aggregate  existences  hv  K  f   n  v  t 
and  »ny  simple  existence  by  A,  we  nnv  Ti.m.  ft.,-™  ""''.\°^  B,  O,  D  t  &c., 

..otnonical  propositions,  alA.,  whic:i,?r:vlTa;;;.:rr:d;rt..r'r'-  "' 
Ther.:fore  similia      ,'^'-<'««:'>""  "J  «  «■'-{  A  are  homo,.. 
Therefore  simiiia  ••  ..  k  ""?  ^ ""-'  """"»• 

Therefore  simiiia  (  -  ..  y  ""    t  T   """""• 

Therefore  simiiia'  "         •'  F  an    t     "  """""• 

A     1  "      I  P  and  A  aie  houion 

And  so  on,  which  i«  a  continued  syllo-rism  or  Soritc.      A  „ 


10-1 
upon  time  and  space;  but  respecting  the  ego  per  se  and  the  non  ego  per  se, 
homon  is  homon  irrespective  of  time.  And  hence  if  we  talie  an  object  as 
time  can  have  no  heterating  effect  upon  it,  a  thousand  years  from  to-day,  it 
will  be  homon;  and  alti\ough  time  has  been  personified  and  endowed  witli 
capacial  grcgaria  by  the  poetg,  it  must  be  evident  that  time  per  se  has  noth- 
ing in  it,  to  produce  any  ef!ect  uptm  the  ego  or  non-ego.  But  as  time  has  no 
capacity  to  heterate  or  differentiate  objects,  it  we  affirm  that  this  where  is  a 
where  of  pure  space,  i.  e.,  this  where  and  one  whereof  pure  space  are  homon, 
and  that  where  and  a  where  of  pure  space  are  homon,  it  must  follow  tli^il  this 
where  and  that  where  are  similia.  If  time  per  se  can  neither  heterate  n«r 
dilferentiafe,  any  two  wheres  of  pure  space  are  now,  always  have  been,  and 
always  will  be,  Similia,  so  long  as  pure  space  and  pure  space  are  homon ;  and 
so  also  with  every  other  object  &o  far  as  time  per  se  i«  concerned. 

But  we  may  ask  ourselves,  has  space  any  capacial  gregaria  to  aflect 
•bjects  occupying  it?  And  by  the  artificial  production  of  a  vacumm,  we 
are  able  to  decide  upon  reflection  that  here,  in  this  instance,  is  a  space,  which 
has  no  capacity  to  interfere  in  any  manner  with  objects  occupying*  it,  were 
aiy  object  in  it.  But  if  hwmon  is  homon,  if  space  is  space,  this  particular 
vacuated  space  and  an}'^  other  where  of  pure  space  are  similia,  they  cannot  be 
differentia,  aLd  hence  no  space  can  heterate,  differentiate  or  iucommensuraie 
objects  occupying  it.  We  have  therefore  eliminated  time  and  space,  as  agents, 
from  our  consideration;  but  before  proceeding  farther,  we  must  explain  some 
terms,  which  we  will  have  occasion  to  use  hereafter. 

If  we  take  any  homon,  this  homon  to-day,  will  be  homon  a  thousand 
years  hence,  so  far  as  time  and  space  are  concerned,  we  will,  therefore,  call 
this  homon  an  homonical  homon.  But  if  we  take  another  homon,  a  like 
case  will  be  with  it,  and  to  distinguish  thc^  second  liomou  from  the  first,  we 
will  call  it  an  hetcrical  homon ;  an  homonical  homon  and  an  heterical  Lomou 
will  then  be  heiera. 

Again;  If  the  homonical  homon  and  the  heterical  homon   be  inter  se 

similia,  we  may  call  the  heterical  homsn  with  reference  to  the  homonical 

homon,  a  similical  homon.  An  homonical  homon  and  a  similical  homon 
will  then  be  similia. 

Again;  If  the  homonical  homon  and  the  heterical  homon  be  inter  sc 
differentia,  we  may  call  the  heterical  homon  with  reference  to  the  homonical 
homon,  adifferential  homon.  An  homonical  homon  and  a  differential  homon 
will  then  be  differentia. 

Again;  If  the  homonical  homoaand  th(/heterical  homon  be  comraen- 
aura,  we  may  call  the  heterical  homon  a  commensural  homon.  An  homoni- 
cal hom«n  and  a  commensural  homou  will  then  be  commensura. 

But  again;  If  the  homonical  homon  and  the  heierical  homon  be  in- 
commensura,  we  may  call  the  heterical  homon,  an  iucommensural  homon. 
An  homonical  homon  and  an  incommeusural  homon  will  then  be  iu- 
commensura. 


♦  105 

The  following  list  will   show  the  terms  and  the  manner  in  which  ihey 
distinguish  objects:  ... 

i_.       H«)moniCHl  homon-  a  }  , 

^^^-      Homonical  homon-a  )"  ''''"^'»" 


hetera. 


2^^        Homonical  homon — a  ) 
Heterical     homon— b  j" 

q,i        Homonical  homon — a)    .     ... 
"^^        Similical    homon— a'  p""'''*- 

A.,.        Homonical  liomon- a  /   .-a. 

*"*•      Differential  homon-b  [  ^'^  rentia. 


Homonical     honum  —  2   } 
Commensural  honioa — 2'  f 


oth.      r^  .  .  -       r   ^commensura. 

Qjlj       Homoniciil      homon  —  2  ) 


Iucommensural  homon— 3  )  '"^ommensura. 
Now  with  the  above  terms,   the  following  syllogisms  which   we  call 
singular  homonical  syllogisms,  because  one  premise  at  least  in  each  mode  is 
homonical,  maj' be  constructed: 

MODE    IST. 

The  homonical  hoinon  a,  in  the  place— b  to-day,  and  the  homonical 
homon— A,  in  any  where  a  thousand  years  hence,  are  homon. 

The  homonical  homon— a',  in  the  place— c  to-day,  and  the  homonical 
homon— A  \  a  thousand  y^ars  hence  in  any  where  are  hoinon. 

Therefore  the  homonical  homon— a,  in  any  wheire  a  thousand  years 
hence,  and  the  homonical  homon  a,  in  any  where  a  thousand  venra  benco, 
aie  similia,  . 

MODE  2d. 

The  iiomonical  homon— a,  in  the  where  b,  to-day,  and  the  homonical 
homon— a,  in  any  where  a  thousand  years  hence,  are  homon. 

The  homonical  homon— a,  in  the  where»  b  to-day,  aod  the  hetericlU 
homou  c,  in  the  where— d  to-day,  are  heiera. 

Therefore  the  homonical  liomon— a,  in  any  where  a  thousand  years 
hence,  and  the  hettrical  homon  c.  iu  anywhere  a  thousand  years  hence, 
are  hetera. 

mod£  3d. 

Tlie  homonical  homon  a  in  the  where  b  to-day,  and  the  homcmical  ho- 
mon A  In  any  where,  a  thousand  years  hence  arc  homon. 

The  liomon  cal  homon  a  io  the  where  b  to-day,  and  the  similical  ho- 
mon A'  in  the  where  c  today  are  similia.  ,.j^ 

Therefore,  the  homonical  homon  a  in  any  where  a  thousand  yefiff 
hence,  and  the  similical  homou  a'  in  any  where  a  thousand  year*  hence,  aie 
similia,  \ 

mode  4th. 

The  homonical  hom^n  a  in  the  where  b  to-day,  and  the  homonipal 
homon  a  in  any  where  a  thousand  years  hence  are  homon. 


106  » 

The  homonical  homou  a  in  the  where  b  to-day,  and  the  diftVrential 
homoD  c  in  the  where  d  to-day  are  differentia. 

Therefore  the  homonical  homon  a  in  any  where  a  thousand  years 
hence,  and  the  differential  homon  c  in  any  where  a  thousand  years  hence  are 

differentia. 

MODE  5rH. 

The  homonical  homon  a  in  the  where  b  to-day,  and  the  homonical  ho- 
mon A  in  any  where  a  thousand  years  hence  are  homon. 

The  nomonical  homon  a  in  the  where  b  to^ay  and  the  commcnsural 
homon  a'  in  the  where  c  to-day,  are  commensura. 

Therefore  the  homonical  homon  a  in  any  where  a  thousand  years  hence 
and  the  commensural  homon  a'    in  any  where  a  thousand  years  hence  are 

commensura. 

MODE  6th. 

The  homonical  liomon  a  in  the  where  b  to  day  and  the  homonical 
homon  a  in  any  where  a  thousand  years  hence  are  homon. 

The  homonical  homon  a  in  the  where  to-day  and  the  incommensural 
homoD  c  in  the  where  d  to-day,  are  incouimensura. 

Therefore,  the  homonical  homon  a  in  any  where  a  thousand  years 
hence,  and  the  incommensural  homon  c  in  any  where  a  thousand  years  hence, 
arc  iocommensura. 

After  a  careful  study  of  the  above  mode  in  the  singular  homonical 
syllogism,  the  following  reasoning,  we  believe,  will  appear  obvious.  If  we 
let  a  homon,  always  be  homon  in  our  minds,  and  we  make  this  homou  a 
SIMILE,  i.  e.,  it  the  homon  a  in  the  where  b,  have  a  simile  in  the  where  c,  and 
another  in  the  where  d  and  so  on,  each  one  of  these  similia  must  have  a  com- 
mon name,  and  no  matter  if  their  heterical  number  be  infinite  and  the  points 
Ib[  time  of  some  be  in  the  past,  of  others  in  the  present,  and  of  still  others  in 
the  future,  yet  we  have  no  hesitation  in  belicvinj;  that  each  one  must  be  an  a, 
tor  if  it  should  not  be  so,  homon  would  not  be  homon ;  and  that  the  really 
aame  thing  ihould  not  be  the  same  thing  is  absurd  and  impossible.  But  the 
homon  in  our  minds  has  a  simile  in  the  minds  of  other  men,  and  hence  wc 
believe  without  a  doubt  that  two  beings  like  ourselves  a  thousand  years  hence 
all  colors,  which  they  will  know  any  thing  about,  will  be  visible,  i.  e.,  color 
and  visibility  will  be  to  them  homon.  The  same  thing  is  the  same  thing, 
hom«D  is  homon,  no  matter  about  the  modifications  of  time  and  space.  Color 
and  visibility  are  homon,  visibility  and  visibility  are  homon.  Therefore, 
color  and  visibility  are  similia  (mode  1st)  as  the  must  be,  if  the  risibility,  in 
tke  first  premise  and  that  in  the  second  be  objectively  hetera;  and  two  ob- 
jectively heterical  existences,  one  in  each  premise,  must  always  be  found  in 
the  premises  of  every  syllogism.  And  hence  the  general  proposition  that  all 
colors  are  visible,  is  established  beyond  a  doubt  by  the  syllogistic   process. 


107 

The  proposition  that  all  sounds  are  audible,  or  that  sound  is,  has  been,  and 
ever  will  be  audible,  is  established  in  the  same  manner.  And  thus  we  may 
deal  with  all  the  homonical  propositions  in  which  both  the  subject  and  pre- 
dicate are  the  simple  existances,  which  we  have  called  facial  gregaria.  That 
all  red  is  red,  that  all  sweet  is  sweet,  or  that  all  white  is,  has  been,  and  ever 
will  be  white  lo  human  beings,  nobody  doubts,  because  a  contrary  supposi- 
tion is  not  only  inconceivable  but  impossible,  unless  similia  and  differentia 
are  homon. 

'  Let  us  now  turn  ouf  attention  to  capacial  gregaria,  and  we  will  first 
notice  figure  or  form.  It  is  a  proposition  not  worth  discussing  after  what 
has  already  been  said  respecting  homonical  propositions  and  space,  that 
every  a^igregate  existence  must  have  some  figure  or  form.  But  were  ten 
milliens  of  forms  inter  se  differentia  known  to  our  minds  (and  about  thin^i 
unknown  we  cannot  reason)  and  we  should  give  a  name  to  distinguish  any 
one  figi  re  or  form,  each  other  figure,  which  was  a  simile  of  the  figure  named 
must  receive  the  name  given  to  the  homonical  figure,  which  name  now  be- 
comes a  common  name  for  all  similia.  If  for  instance  we  distinguish  from 
other  things  any  round  ring  by  the  name  CIRCLE,  then  any  round  ring  thus 
distinguished  from  oth2r  things,  has  been,  is  aud  always  will  be  a  circle 
First  round  ring  aud  a  circle  are  homon,  second  round  ring  and  first  are 
similia.  Therefore  sec(>nd  round  ring  aud  a  (one)  circle  are  homon.  And  8  » 
also  with  squares,  cubes,  triangles,  parallelograms,  <S:;c. 

And  it  must  be  evident  that  if  in  any  relation  of  parts,  anything  which 
may  be  called  a  quality,  be  found  in  any  figure,  this  quality  must  have  a 
simile  in  any  other  fiujure,  which  is  a  simile  of  the  first  figure.  F«r,  all  the 
relations  of  the  space  inclosed  by  the  outlines  of  any  figure,  must  be  inclosed  in 
like  manner  by  the  outlines  of  all  figures  which  are  inter  se  similia.  Certain 
points  and  their  relations  inter  se  in  space  constitute  a  figure,  and  when  we  lay 
down  all  the  points  and  tueir  relations,  which  that  figure  can  contain.  One  cir- 
cle and  another  are  similia,  the  commensural  relation  of  the  diameter  and  one 
third  of  the  circumference  is  in  the  fiist  circle,  i.  e.,  the  where  of  such  com- 
mensural relation  of  points  in  space  and  the  where  of  the  points  contained 
in  the  first  circle  are  homon,  therefore  this  commensural  relation  is  in  the 
second  circle:  and  as  circles  are  similia  oi  space,  tbij  relational  simile  is  in 
all  circles  at  any  time  in  any  where.  And  such  is  the  case  with  all  the  geo- 
metrical figures. 

But  if  we  onsider  the  forms  of  animals,  vegetables  or  minerals,  we 
will  find  but  few  perfectly  similia.  The  human  torm  has  no  homonical 
standard  by  whicii  to  determine  similia.  If  we  should  give  certain  and 
definite  relations  of  points  in  space  as  the  human  form,  we  then  might  reason 
wpon  such  human  form  with  logical  mathematical  certainty,  but  our  reason- 
ing would  only  be  approximately  true  when  applied  actually  to  individuals. 


For  tlie  homonical  standard  which  we  have  asRumed,  lias  not  a  simile  in 
each  iadividual  of  mankind;  yd  there  is  an  approximaiion  to  similiii  in  the 
forms  of  human  beings  sufficient  usually  to  distinguish  the  human  form  from 
that  of  other  animals.  And  this  sufficient  approximation  lo  an  homonical 
standard  in  one  spaces,  and  the  approximation  t(»  an  homonical  standard  in 
another,  enable  us  to  affirm  differentia  anywhere,  now,  in  time  past,  and  in 
the  future.  We  may  say  with  all  confidence  that  the  form  of  any  man  and 
the  form  of  any  lizzard  are.  have  been  and  always  will  be  differentia.  The 
human  form,  tlioagh  not  a  simile  oi  any  homonical  standard,  is  sufficiently 
distinguished  by  its  relations  from  others;  and  were  it  not,  so,  we  could  not 
tell  the  human  form  from  others.  We  can  not,  indeed,  point  out  any  particu 
lar  in  the  form  of  John,  and  say  that  wherever  man  is  found,  you  will  tind  n 
simile  of  this  particular,  but  we  can  point  out  a  number  of  particulars  in 
John  and  say  with  confidence  that  wherever  man  is  man  there  will  be  an  ap- 
proximation to  these  particulars.  Of  the  forms  of  animals,  vegetables  and 
minerals  then,  we  can  not  usually  find  an  homonical  type,  and  hence  we  can 
draw  but  approximate  conclusions  respecting  the  individuals  which  we  have 
not  seeq. 

Let  us  next  consider  impenetrability.  We  my  and  believe  that  all  mat- 
ter is  impenetrable;  and  impenitrability  being  a  simple  existence  and  the 
predicate  of  an  homonical  proposition  whose  subject  k  an  aggregate  exis- 
tence, we  mean  of  course,  that  one  of  the  gregaria  sine  qua  uou  of  matter 
and  impenitrability  are  homon.  And  why  do  wc  believe  this?  Simply  b» 
cause  we  believe  that  homon  is  homon  in  any  where  at  any  time.  Take  the 
proposition  All  matter  occupies  space;  and  if  this  needs  proof,  we  may  take 
any  piece  of  matter  and  we  will  see  thai  this  piece  occupies  space;  we  will 
see  also  that  a  where  occupied  and  a  where  unoccupied  are  differentia;  then 
the  where  of  this  piece  of  matter  and  an  occupied  where  are  homon;  an  un- 
occupied where  and  an  occupied  where  are  differentia;  but  if  another  piece 
of  matter  can  exist  in  an  unoccupied  where,  then  the  where  of  the  first  piece 
and  the  where  of  the  second  one  are  differentia.  But  all  unoccupied  wheres 
in  space  are  similia,  because  space  is  space,  homon  is  homon;  the  capacity  to 
occupy,  therefore  in  any  where,  is  the  only  thing  that  can  make  an  occupied 
where  and  an  unoccupied  where,  differentia.  But  this  capacial  gregarium 
must  reside  in  the  thing  occupying,  and  therefore  matter  having  this  grega- 
rium and  matter  without  it  are  differentia.  But  matter  is  matter,  homon  is 
homon,  and  this  capacial  gregarium  is  the  sine  qua  non,  which  makes  difler- 
eat  pieces  of  matter  similia,  and  therefore  all  matter  must  occupy  space. 
Impenitrability  in  objects  is  nothing  more  than  the  capacity  to  remain  in 
space;  for,  so  long  as  an  homonical  obejct  remains  in  8i)ace,  the  homonical 
where,  in  which  it  is,  cannot  be  occupied  by  an  heierical  object,  unless  hetera 
and  homon  are  homon,  which  is  impossible.    So  long  therefore,  as  matter  is 


109 
matter,  impenitrability  will  be  its  capacial  gregarium.  That,  which  has  no 
where,  cannot  be  matter,  and  hence  matter,  whose  impenitrabiljlty  has  been 
destroyed,  is  no  longer  matter,  it  is  no  longer  anything.  The  homonical 
where  of  an  homonical  existence  called  matter  and  xn  (one)  occupied  where 
are  homon,  an. occupied  where  and  an  unoccupied  where  are  differentia;, but 
if  the  homonical  matter  in  the  homonical  where  be  destroyed  by  heterical 
matter,  the  homonical  where  cannot  be  occupied  by  the  homonical  nxatter 
unless  hetera  and  homon  are  homon,  which  is  impossible;  therefore  any  mat- 
ter must  occupy  space.  This,  however,  does  not  proye  that  matter  cannot  be 
annihilated;  it  only  proTcs  that  wherever  and  whenever,  matter  is  matter,  it 
will  occupy  space ;  that  all  matter  is  impenitrable.  Whether  matter  can  be 
annihilated  or  not,  we  have  no  data  from  which  we  can  decide  the  question. 
Water  may  be  inclosed  in  a  golden  ball  and  pressed  through  the  gold,  but 
this  only  proves  that  by  such  means  matter  cannot  be  annihilated. 

The  use  of  the  syllogistic  process  in  establishing  a  sine  qua  non,'t>jr'the 
BIN0T7LAR  HOMONICAL  SYLLOGISM,  which  WC  have  just  been  discussing,  seiems 
to  be  what  J.  Stuart  Mill  considers  the  true  type  of  induction,  when  he  de- 
fines induction  lo  be  "the operation  of  discovering  and  proving  genera!  pro- 
positions." Mr.  Mill,  however,  like  all  other  writers  upon  induction,  leems 
to  have  had  no  definite  conception  of  the  thing  for  which  he  was  on  the  look- 
out, and  he  would  not  have  been  able  to  have  identified  it,  if  he  had  found  it. 
In  one  place  induction  is  "the  operation  of  discoverinf^  and  proving  general 
propositions;"  in  an  other  it  is  "generalization  from  experience;"  in  an  other 
it  is  "that  operation  of  the  mind  by  which  we  infer  that  what  wc  know  to  be 
true  in  a  particular  case  or  cases,  will  be  true  in  all  cases  which  resemble  the 
former  in  certain  assignable  respects;"  and  again,  "to  ascertain  what  are  the 
laws  of  causation  which  exist  in  nature;  to  determine  the  effects  of  eyery 
cause,  and  the  caiises  of  all  effects,  is  the  main  business  of  induction ;  and  to 
point  out  how  this  is  done  is  the  chief  object  of  inductive  logic."  Mr.  Mill 
is  an  able  writer,  but  his  logical  induction  is,  in  a  great  measure,  an 
ignus  fatuus. 

CHAPTER  XXII. 

,  THE    PLURAL  HOMONICAL   SYLLOGISM.        ,     „•    ,,.  .^  ;  ._, 

Having  shown  in  the  last  chapter  how  we  generalize  from  experience, 
and  also  how  in  certain  cases  we  may  select  a  simple  homonical  existence 
and  prove  it  to  be  a  sine  qua  non  by  the  singular  homonical  syllogism,  we 
must  pursue  the  syllogistic  process  still  further  and  show  how  wo  reason  by 
the  Plural  Homonical  Syllogism,  if  we  put  two  balls  before  us,  we  will 
say  that  they  are  hetera,  i.  e.,  that  the  one  is  not  the  other;  if,  however,  we 
turn  our  eyes  away  from  them  for  a  few  moments,  or  cover  iheix^  with  our 
hand,  and  then  we  remove  it  from  them  and  look  at  them  again,  we  will  say^ 


no 

that  they  are  the  same  balls.  But  by  this  expression  we  do  not  mean  Ihali 
the  one  and  the  other  are  homon,  for  we  know  that  inttr  se  \hey  are  hetera, 
but  what  we  really  mean,  is,  that  the  two  balls  under  our  eyes  then  aie  the 
identical  balls  under  our  eyes  now,  i.  e.,  the  two  balls  then  and  the  two  ballrj 
NOW  are  homonical  hetera.  And  before  proceeding  further,  we  must  again 
explain  some  terms,  which  we  will  have  occasion  to  use  in  our  future 
inquiries. 

We  hare  already  seen  that  time  aud  space  per  se  have  no  capacity  to 
heteratt,  differentiate  or  incommensurate  objects  in  time  and  space,  that  sub- 
jectively two,  but  objectively  one  homonical  ball  te  day,  so  far  as  time  and 
space  per  se  are  concerned,  will  be  objectively  homon,  to-morrow  and  for- 
ever; we  will  therefore  call  such  homa,  homonical  homa.  But  if  we  take 
subjectively  two  other  balls,  which  are  objectively  hemon,  they  are  related  to 
themselves  in  like  manner  as  the  first  two,  we  will  call  them  heterical  homa: 
Homonical  homa  and  heterical  homa  will  then  be  hetera. 

A^ain,  If  two  homonical  hetera  be  inter  se  hetera  to-day,  so  far  as 
time  and  space  are  concerned,  they  will  remain  hetera,  and  therefore  we  will 
call  them  homonical  hetera;  but  if  we  take  two  other  hetera,  they  also  will 
remain  hetera,  and  to  distinguish  them  from  the  first  two,  we  will  call  them 
hewrical  hetera:     Homonical  hetera  and  heterical  hetera  will  then  be  hetera. 

Again,  If  twe  homonical  lietera  be  inter  se  similia  to-day,  so  far  as 
time  and  space  are  concerned,  they  will  remain  similia  inter  se,  and  therefore 
we  will  call  them  homonical  similia  ;  but  if  we  take  two  heterical  hetera 
inter  se  similia,  they  also  will  remain  inter  se  similia,  and  to  distinguish  them 
from  the  first  two,  we  will  call  them  heterical  similia:  Homonical  similia 
and  heterical  similia  will  then  be  hetera. 

Again,  If  we  take  two  homonical  hetera  inter  se  differentia,  they  will 
remain  differentia,  and  we  will  call  them  homonical  differentia;    but  if   we 
take  two  other  hetera  inter  se  differentia,  they  alse  will    remain  differentia, 
and  to  distinguish  them  from  the  first  two,  we  will  call  them  heterical  difier 
entia:    Homonical   differentia  and  heterical  differentia  will  then   be  hetera. 

Again,  If  we  take  two  homonical  hetera  inter  se  commcusura,  they 
will  remain  inter  se  commensura,  and  we  will  call  them  homonical  commen- 
sura;  but  if  we  tak6  two  other  hetera  inter  se  commensura,  a  like  crise  will 
be  with  them,  and  to  distinguish  them  from  the  first  two,  we  will  call  them 
heterical  commensura:  Homonical  commensura  and  heterical  commensura 
will  then  be  hetera. 

Again,  If  we  take  two  homonical  hetera  inter  se  incommensura,  they 
will  remaim  incommensura,  and  we  will  call  them  homonical  incommensura; 
but  if  we  take  tw*  other  hetera  int-er  so  incommensura,  a  like  case  will  be 
with  them,  and  to  distinguish   them  fr«m   the  first  two,  we  will  call   them 


lU 
heterical  incommensura;  Homonical  incommensura  and  heterical  incom- 
mensura wfll  then  be  hetera. 
« 

Again,  If  we  take  two  hetera  inter  se  similia,  they  will  remain  inter 
se  similia,  and  we  will  call  them  homonical  similia;  but  if  now  we  take  two 
heterical  similia,  and  the  homonical  similia  and  heterical  similia  be  inter  te 
similia,  to  distinguish  the  heterical  similia,  we  will  call  them  similical 
bimilia:    Homonical  similia  and  similical  similia  will  then  be  similia. 

Again,  It  we  take  two  homonical  similia  and  two  heterical  similia, 
and  the  homonical  similia  and  heterical  similia  be  inter  se  differentia,  we 
will  call  the  latter  differential  similia;  Homonical  similia  and  differential 
similia  will  then  be  differentia. 

Again,  If  we  take  two  homonical  differentia  and  two  heterical  differ- 
entia, and  the  one  of  the  homonical  differentia  and  one  of  the  heterical  differ- 
entia be  inter  se  similia,  and  the  other  of  the  homonical  differentia  and  the 
other  of  the  heterical  differentia  be  inter  se  similia,  we  will  call  such  heter- 
ical differentia,  similical  ditterentia:  Homonical  differentia  and  similical 
differentia  will  then  be  similia. 

Again,  If  we  take  two  homonical  differentia  and  two  heterical  differ- 
entia, and  the  homonical  differentia  and  heterical  differentia  be  inter  se  dif- 
ferentia, we  will  call  such  heterical  dift'erentia,  differential  differentia:  Ho- 
monical difl'erentia  and  differential  differentia  will  then  be  differentia. 

Again,  If  we  take  two  homonical  commensura  and  two  heterical  com- 
mensura, and  they  be  inter  »e  commensura,  we  will  call  the  latter  commen- 
sura, commensural  commensura:  Homonical  commensura  and  commensural 
commensura  will  then  be  commensura. 

Again,  If  we  take  two  homonical  commensura  and  two  heterical 
commensura,  and  they  be  inter  se  incommensura,  we  will  call  the  latter,  in- 
commensural  commensura:  Homonical  commensura  and  incemmensural 
commensura  will  then  be  incommensura. 

Again,  If  we  take  two  homonical  incommensura  and  two  heterical 
incommensura,  and  the  one  of  the  homonical  incommensura  and  one  of  the 
heterical  incommensura  be  inter  se  commensura,  and  the  other  of  the  ho- 
monical incommensura  and  the  other  of  the  heterical  incommensura  be  inter 
se  commensura,  we  will  call  the  heterical  incommensura,  commensural  incom- 
mensura: Homonical  incommensura  and  commensural  incommensura  will 
then  be  commensura. 

Again,  If  we  take  two  homonical  incommensura  and  two  heterical 
incommeusura„and  they  be  inter  se  incommensura,  we  will  call  the  latter, 
incommensural  incommensura:  Homonical  incommensura  and  incommen- 
sural  incommensura  will  then  be  incommensura. 


118 


The  following  list  will  show  the  terms  ♦nd  their  relations: 


^     Homonical  homa  a.a.  Ij^Qm^ 

Homonical  homa  a.a.  f 
'     JJomomcalhomaa.a..U^j^,j.^ 
**   Hetcncal  homa  a. '  a. '  ) 


9    ST°°'f  *i  '•™-l-*  K  K*  f  differentia. 
^'  Differential  similia  b.b. ) 


^rt  Homonical  differentia  a.b.  Ift;-,;i;- 
^^  Similical  differentia  a.'b.'  p^™*"* 

-    Homonical  diffcremia  a.b.  Ugtera  13  P'^*^^^  ^°°^' o'H  incommensura. 
^-    Heterical  differentia  c.d.     i  'i*^''^^*-  ^^  Incom.  com.  3.3.  J 

g    Homonical  comensura  2.3.  {  ^etera.U  ^ZilTcoT^I^"  [  commenaura. 
Heterical  commensura 3.3.  )  Com.  incom.-i.d.    ) 

,''*H«monicalincomens'a2.3.  ^  ijetera  15  ?°"-  i^.^*^^- 2-^'     j.  incommensuru 
^'   Heterical  incem'ensura  3.4  f  "*'**'^'' '''  Incom.  mcom.  6.6.  S 

8    S^°?*°'^*^.  ^^ M-^^^'*  *•*;  ^  similia. 
^'   Similical  similia  a.a.'  i 

Now  the  following  paradigms  will  show  the  syllogisms,  which  may 
be  constructed  with  the  foregoing  terms,  which  syllogisms,  as  they  have  one 
homonical  premise  at  least  in  each  mode,  we  call  plural  homonical 
syllogisms. 

Mode  First.— The  homonical  homa  a.a.  to-day,  and  the  homonical 
homa  a.a.  a  thousand  years  hence,  are  homonical  homa;  The  homonical  a' a 
to-day  and  the  homonical  homa  a.  a.'  a  thousand  years  hence  are  homonical 
hotoa ;  Therefore  the  homonical  homa  a.a.  a  thousand  years  hence  and  the 
het<>rical  ht>ma  a.  a.'  a  thousand  years  hence,  are  similical  homa. 

Mode  Second— The  homonical  homa  a.a.  to-day,  and  the  homonical 
homaa.a.  a  thousand  years  hence,  are  homa;  The  heterical  homa  a. 'a.'  to- 
day and  the  homonical  homa  a.a.  to-day,  are  heterical  homa;  1  heretore,  the 
homonical  homa  a.a.  a  thousand  years  hence,  and  the  heterical  homa  a. 'a.'  a 
thousand  years  hence,  are  heterical  homa. 

Mode  Third.— The  homonical  hetera  a. 'a  to-day,  and  tho  homonical 
hetera  a  a.  a  thousand  years  hence,  are  homonical  hetera;  The  homonical 
hetera  a.  a.  to-day,  and  the  heterical  hetera  b.b.  to-day,  are  heterical  hetera; 
Therefore,  the  homonical  hetera  a.  a.  a  thousand  years  hence,*and  the  heteri- 
cal hetera  bb,  a  thousand  years  hence,  are  heterical  hetera. 

ModeFourth.— The  homonical  similia  a.a.  to-day,  and  the  homonical 
similia  a.a.  a  thousand  years  hence,  are  homonical  similia;    The  homonica 
similia  a-a.  to-day,  and  the  heterical   similia  a.  a.'    to-day,  are  heterical 
similia;  Therefore  the  homonical  similia  a.a.  a  thousand  years  hence,  and  the 
hetericjil  similia  a.  a.'  a  thousand  years  henco  are  heterical  similia. 

Mode  Fifth.— The  homonical  differentia  a.b.  to-day,  and  the  homonical 
differentiaa.b.  a  thousand  years  hence  are  homonical  differentia;  The  ho- 
monical differeatia  a.h.  to  day,  and  the  heterical  differentya  c.d.  to-day  are 
haterical  differentia;  Therefore  the  homonical  differentia  a.b.  a  thousand 
years  hence,  and  the  heterical  diffcicn^ja  c.d.  a  thousand  years  hence,  are 
heterical  differentia. 


113 

Modo  Sixth. — The  homonical  commensura  3.2.  to-day,  and  tke  homon- 
ical commensuTa  3.2.  a  thousand  years  hence,  are  homonical  commensura; 
The  homoDical  commensura  3.3.  to-day,  and  the  heterical  commensui:a  3.3. 
to  -day  are  heterical  commensura ;  Therefore  the  homonical  commensura  3.3. 
a  thousand  years  hence,  and  the  heterical  commensura  3.3.  a  thousaud  years 
hence,  are  heterical  commensura. 

Hode  Seventh. — The  homonical  iacommensura  3.3.  to-day,  and  the 
homonical  incpmmensura  3.3.  a  thousand  years  hence  are  homonical  incom- 
mfusura;  The  homonical  incommensuru  3.3.  to-day,  and  the  iieterical  incom- 
mensura  4.5.  to-day  are  heterical  incommensura;  Therefore  the  homonical 
incommensura  3.3.  a  thousand  years  hence,  and  the  heterical  incommensura 
4.5.  a  thousand  years  hence,  are  heterical  incommensura. 

Mode  Eighth. — The  homonical  similia  a.a.  to-day,  and  the  homonical 
similia  a.a.  a  thousand  years  hence,  are  homonical  similia;  The  similical 
similia  a.  a.'  to  day  and  the  homonical  similia  a.a.  to-day  are  similical 
similia;  Therefore  the  homonical  similia  a.a.  a  thousand  years  hence,  and 
the  similical  similia 'a. 'a,'  a  thousand  years  hence  are  similical  similia. 

Mode  Ninth. — The  homonical  similia  a.a.  to-day,  and  the  Jiomonical 
similia  a.a.  a  thousand  years  hence  are  homonical  similia;  The  homonical 
similia  a.a.  to-day,  and  the  differential  similia  b.b.  to-day,  are  differential 
similia;  Therefore  tlio  homonical  similia  a.a.  a  thousaud  ye*^ars  hence  and  the 
differential  similia  b.b.  a  thousand  years  hence  are  differential  similia. 

Mode  Tenth. — The  homonical  differentia  a.b.  to-day  and  thehomon]cal 
differentia  a.b.  :i  thousand  years  hence  are  homonical  differentia;  The  homon- 
cal  differentia  a.b.  to-day,  and  tbe  similical  differentia  a.'b.'  to-day  are 
similical  ditferentia;  Therefore  the  homonical  differentia  a.b.  a  thousand 
years  hence,  and  the  similical  differentia  a.  b.'  a  thousand  years  hence,  are 
similical  differentia. 

Mode  Eleventh — The  homonical  differentia  a.b.  to-day,  and  the  ho- 
monical differentia  a.b.  a  thousand  yeurs  hence  are  homonical  difterentia;  The 
differeniial  differentia  c.d.  to-day,  and  the  homonical  differentia  a.b.  to-day 
are  differential  differentia;  Tiierefore  the  differential  differentia  c.d.  a  thous- 
aud years  hence,  and  the  homonical  dift'erentia  *;.b.  a  thousand  years  hence 
are  differential  differentia. 

Mode  Twelfth.- The  homonical  commensura  3.3.  to-day,  and  the  ho- 
monical commensura  3.3.  a  thousand  years  hence,  are  homonical  commen- 
sura; The  commensural  commensura  3. '3.'  to-day,  and  the  homonical  com 
mensura  3.3.  to-:day,  are  commensural  commensura;  Therefore  tlie  commen- 
sural  commensura  3. '3.'  a  thousand  years  hence,  and  the  homonical  com- 
mensura 3.3.  a  thousand  years  hence,  are  commensural  commensura. 

Mode  Thirteenth. — The  homonical  coyimensura  3.3.  to-^ay,  and  the 
lioraonical  commensura  3.3.  a  thousand  years  hence  are  homonical  com- 
mensura; The  incommeusural  commensura  3.3.  to-day,  and  the  homonical 
commenaura  2.3.  to-day,  are  incommeusural  commensura;  Therefore  the  in 
commensural  commensura  3.3.  a  thou.sand  yeais  hence,  and  the  homonical 
commensura  3.8.  a  thousand  years  liecce,  are  iucommensural  commensura. 

Mode  Fourteenth.— The  homonical  incommensura  3.3.  to-day,  and  the 
homonical  incomraensur  3.3.  a  thousaud  years  hence, 'are  homonical  ihcom- 
uieusura;  The  commensural  incommensura  3.'??.'  to-day,  and  the  homonical 
incommensura  3.3.  to-day,  are  commensural  incommensura;  Therefore  the 
commensural  incommensura  3. '3.    a  thousand  years  hence,  and  the  homoni- 


114 

cal  incommensura  2.3.  a  thousand  years  hence,  are  commcusural  incom- 
mensura.        . 

Mode  Fifteenth.— The  homonical  incommensura  2.8.  to-day,  and  the 
homonical  incemmeusura  2.3.  a  thousand  years  hence,  are  homonical  incom- 
mensura; The  incom^ensural  incommensura  5.6.  to-day,  and  the  homonical 
incommensura  2.3.  to-day,  are  incommensural  incommensura;  Therefore  the 
incommensural  incommensura  5.6.  a  thousand  years  Jience,and  the  iiomonical 
incommensura  2.3.  a  thousand  years  hence,  are  incommensural  incommensura. 

If  the  reader  has  carefully  studied  what  we  have  called  the  singular 
homonical  syllogism  in  the  proceeding  chapter,  the  plural  homonical  syllo- 
gism will  not  need  to  be  specifically  explained.  And  any  person  can  see  thac 
we  are  not  necessarily  limited  to  two  homa  or  helera;  we  may  take  the  ho- 
monical homa  or  hetera  a,  b,  c,  d,  e,  &:c.,  and  deal  with  them  in  like  manner 
as  we  have  dealt  with  two  homa. 

Now  if  we  take  any  simple  existence  in  nature,  any  one  will  allow  that 
this  simple  existence  and  itself  are  homon ;  and  any  one  will  agree  also  that  so 
l«ng  as  this  simple  existence  and  itself  arc  homon,  it  and  itself  can  not  be 
hetera,  and  consequently  it  can  not  be  a  simile  of  itself,  nor  can  it  and  itself 
be  differentia.  And  in  a  previous  chapter  we  have  shown  that,  when  wc  look 
upon  nature,  we  gain  our  knowledge  of  cause,  in  the  first  instance  through 
effects,  which  arc  manifested  by  changes.  And  from  what  we  have  said 
already,  it  must  appear,  that  a  homon  per  se  can  not  change:  whalev..r  it  may 
be,  so  long  as  it  exists,  it  is  the  homonical  homon.  If  then  we  take  any  sine 
qua  non,  impenitrability  for  instance,  this  sine  qua  non  isimpenitrability  to- 
day, always  has  been  and  always  will  be,  homon  is  hoinou. 

Now  if  we  place  before  us  an  ivory  ball,  wu  hare  no  dowbls  in  affirm- 
ing that  one  of  the  capacial  greguria  sine  qua  non  of  lhi&  ball  and  impenetra- 
bility are  homcm;  and  it  we  put  before  us  another  ivory  ball,  we  will  make  a 
ike  affirmation  respecting  it,  and  therefore  the  first  and  second  balls  are 
similia.  And  if  the  first  gregarium  be  located  in  the  homonical  where  15, 
and  the  second  one  enter  the  homonical  where  B,  the  first  one  must  take  an 
heterical  where.  For,  in  the  respect  of  impenetrability  the  two  balls  are 
similia;  and  therefore  the  homonical  similia  a. 'a.  to-day,  the  one  (a)  in  the 
homonical  where  B,and  the  other  (a')  in  the  where  C,and  the  homonical  sim- 
ilia a. 'a.  to-morrow  in  any  where  are  homonical  similia.  But  respecting  the 
homonical  sifnilia  a.  a.  to-morrT)vv,  if  the  second  (a)  be  in  the  where  B,  i.  e., 
if  the  where  B  occupied  to-day  by  the  first  (a)  to-morrow  be  occupied  by  the 
second  (a.),  the  second  (a.  )  must  have  a  simile  in  the  first  (a),  and  the  where 
of  this  SIMILE,  and  the  where  B  must  be  hetera.  Ikit  if  (a.)  the  first  sine  qua 
non  be  displaced  necessarily  from  the  where  B  by  the  entrance  of  the  .second 
(a.)  sine  qua  non,  is  nof  what  has  happened  in  a  single  instance  sufficient  to 
establish  beyond  a  doubt  that,  whenever  any  w^hekk  is  occupied  by  an  a  and 
another  a'  enters  this  where,  the  first  a  must  be  displaced?  So  long  a.s  homa 
are  homa,  this  mu^f  be  the  case  in  any  part  of   space  at  any  point   of    lime. 


115 

And  if  this  be  the  case  with  the  homonical  similia  a, 'a.,  must  it  not  always 
be  the  case  with  all  similical  similia?  And  if  we  call  this  displacement  of 
one  impenitrable  object  by  an  other,  a  law,  it  must  be  evident  that  this  law 
is  uniform,  i.  e.,  this  law  and  an  uniformity  are  homon.  And  in  a  like  man- 
ner we  might  treat  of  elasticity,  of  fluidity,  of  rigidity,  lubricity  and  so  on- 
And  so  lone  as  homa  are  homa  and  similia  are  similia,  we  can  not  doubt  of 
the  uniformities  in  all  instances. 

But  again  if  we  take  two  differentia,  oxygen  and  hydrogen  for  instance, 
we  may  reason  upon  them  in  like  manner  and  with  perfect  exactness.  For, 
oxygen  being  an  elementary  thing,  so  long  as  oxygen  is  oxygen,  as  homon  is 
hoinon,  any  particular  oxygen  will  contain  all  the  gregaria  of  any  oxygen,  i. 
e.,  each  gregarium  of  a  particular  oxygen  will  have  a  simile  in  any  and  every 
other  oxygen:  and  so  also  with  hydrogen.  And  hence  if  any  homonical  pro- 
cess unite  them  into  water  in  any  instance,  a  aimile  of  this  process  will  unite 
ihem  into  water  in  every  instance.  So  long  as  homa  are  homa,  similia  similia 
and  ditterentia  differentia,  we  can  not  doubt  that  a  result  brought  out  of  the 
homonical  differentia  a.b.  by  the  homonical  process  d,  will  have  a  simile  of 
that  result  brought  out  of  the  similical  ditterentia  a.'b.  by  d',  a  simile  of  the 
homonical  process  d.  And  hence  we  must  conclude  that  The  laws  of  nature 
are  uniform;  is  a  proposition  which  is  established  in  our  minds  by  the  syllo- 
gistic process.  The  result  of  the  homonical  differentia  a.b.  by  the  homoni- 
c.mI  process  d  and  A  are  homon:  The  homonical  ditterentia  a.b.  with  the  ho- 
numical  process  D  and  the  similical  ditterentia  a  'b.'  with  the  similical  pro- 
cess d'  are  similia;  Therefore  the  result  of  the  similical  ditterentia  a.'b.' 
by  the  similical  process  d'  and  a  are  similia. 

We  have  now  said  all  that  we  deem  necessary  to  be  said  at  present 
while  treating  of  the  syllogism.  We  have  given  the  syllogistic  process  a 
much  more  thorough  analysis  than  it  has  received  heretofore  by  writers  upon 
logic,  and  we  h«)pe  that  our  labors  thus  far  will  enable  philosophers  who 
shall  come  after  us  to  see  clearly  the  manner,  application  and  use  of  the 
syllogism.  We,  however,  must  proceed  further,  and  treat  of  induction,  a 
subject,  which,  we  are  confident,  has  not  been  understood  by  writers  upon 
that  subject.     lnducii«)n,  therefore,  will  occupy  our  attention  in  Book  II. 


BOOK  II. 


•■:#»   ,1 


^'H 


,  CHAPTER  I. 

MISNAMED  INDUCTIONS. 

The  processes  of  the  mind  concerned  in  induction,  in  our  apprehend- 
sion,have  not  been  understood  by  any  writer  upon  logic,  with  whose  works 
we  are  acquainted.  Bacon  is  said  to  have  been  the  author  of  the  inductiye 
philosopliy ;  but  his  Novum  Organum  shows  the  necessity  of  such  a  philoso- 
phy scientifically  constructed  rdther  than  the  actual  construction  in  a 
methudical  manner.  His  remarks,  as  far  as  they  go,  are  not  systematically 
arranged,  and  therefore  they  arc  often  obscure;  and  from  this  reason  with 
others,  his  suggestions,  though  frequently  of  the  greatest  importance,  have 
not  led  his  successors  to  glean  from  his  aphorisms  the  true  principles  of  in- 
duction and  to  work  them  into  a  scientific  and  methodical  system  of  inductive 
logic.  That  Bacon  iiad  in  view  a  better  and  greater  systena  of  philosophj 
than  subsequent  writers  have  made  out  of  it  seems  to  me  to  be  certain.  The 
aids  fbr  the  understanding,  about  which  he  speaks  so  frequently,  are  suggested 
here  and  there  in  the  second  book  of  the  Organum,  but  without  any  scientific 
theory  to  cement  und  make  his  remarks  understood.  History  and  experi- 
ments, without  the  knowledge  of  the  inductive  processes  and  their  applica- 
tion can  not  aid  the  understanding  in  gaining  certain  knowledge  of  nature's 
laws;  and  these  processes,  as  far  as  treated  of,  arc  not  brought  out  in  a 
scientific  manner  in  the  Organum.  Men  have  always  had  nature  before  them 
but  the  method  of  interrogating  h«r  has  not  been  understood  And  though 
Bacttn  made  a  grand  beginning  at  explaining  this  method,  yet  most  subse- 
quent writers  have  not  only,  not  improved  upon  Bacon's  work,  but  have 
underated  the  val'te  of  such  method. 

There  is  no  subject  about  which  more  erroneous  notions  prevail  among 
philosophers,  than  about  the  subject  of  the  inductive  processes  themselves; 
and  these  notions,  in  our  opinion,  are  grounded  upon  erroneous  notions 
about  the  syllogism.  Philosophers  are  not  at  all  agreed,  about  what  pro- 
cesses, when  pointed  out  shall  be  called  iaductive;  and  hence  results,  which 
are  entirely  owing  to  the  syllogism,  are  often  claimed  as  inductions,  induction 
having  some  vague  and  unexplained  meaning.  The  better  way,  however,  to 
show  what  results  are  owing  to  the  syllogistic  process,  is  to  explain  the 
syllogism,  and  then  the  reader  himself  can  make  the  application  to  any  case, 
which  may  arise;  this  we  have  endeavored  to  do  heretofore.  And  the  better 
way  to  show  what  results  are  owing  to  the  inductile  processes,  will  be  to 
explain  these  processes.  But  before  doing  this,  from  the  manner  in  which 
the  subject  has  been  treated  by  authors  heretofore,  it  is  neeessar}-,  in  order  to 
be  well  understood  by  the  reader,  for  us  to  show  some  things,  which   have 


been  called  in<liiction,  but  which  in  our  system  do  not  at  all  come  under  the 
meaning,  which  we  attach  to  that  term. 

Archbishop  Wlmtel}-  has  treated  of  induction,  but  bis  erroneous  no- 
tions, as  we  conceive,  of  the  syllogism,  led  him  to  misconceive  the  nature  of 
the  inductive  processes;  thoui^h  maiy  of  his  remarks  are  valuable  in  helping 
to  clear  the  way  for  a  better  understanding  of  the  matter.  The  scholar, 
however,  who  has  done  more,  perhaps,  than  any  wther,  in  clearing  th«  way, 
is  I.  Stuart  Mill.  His  treatise  upon  logic  is  learned  and  able,  though  we 
can  not  agree  with  him  either  upon  ratiocination  or  iaduction.  Archbishop 
Whately  has  well  remarked  that  the  syllogistic  process  is  not  the  sole  process 
ne3essary  in  reasoning  in  a  syllogistic  manner;  and  we  may  stale  that  we  do 
not  consider  the  syllojrislic  and  induetive  processes  together  to  be  the  00I3' 
processes  used  in  gaining  truth,  as  any  one  will  understand,  who  has  studied 
the  remarks  made  in  ihe  chapters  previous  to  those  treating  of  propositions 
and  the  svllogism  in  book  1.  But  to  attempt  to  notice  all  the  procesvses, 
which  hafe  been  brought  forward  as  iuductive,  but  which  we  do  not  regard 
as  such,  would  require  too  much  room  in  this  book,  and  besides,  as  we  think, 
it  will  be  unnecessary. 

And  first,  whe»  a  name  stands  for,  or  points  out  a  sine  qua  non,  which 
distinguishes  the  existence  for  whicli  it  stanils  from  others,  we  d«)  not  con- 
sider that  the  inductive  process  has  anything  to  do  with  proving  this  sine 
qua  noB,  or  with  proving  the  general  proj>osition,  which  may  be  constructed 
upon  this  sine  qua  non.  All  those  truths,  which  we  have  called  nfmiinal 
truths,  are  each  of  them,  a  sine  qua  non  of  themselves;  aud  hence  there  is  no 
indiiction  in  establishing  the  truth  of  the  proposition  that,  every  color,  in 
any  place  at  any  time,  is  a  color,  but  the  tr.Uh  of  such  proposition  is  estab- 
lished by  the  singular  hMm(»nical  syllogism,  as  we  have  shown  heretofore. 
Neither  do  we  consider  induction  to  be  the  collecting  of  a  stUllcient  number 
of  in.stpnces  to  wanaiit  us  in  believing  that  the  instances,  which  we  Imvo 
seen,  are  fair  specimens  of  the  class.  We  should  think  strangely  of  a  man, 
who,  after  having  been  ijiformed  that  the  name  island  distinguishes  a  portion 
of  land  entirely  jsurrounded  by  .vater  shouUI  start  on  a  tour  to  examine  this 
and  that  island,  until  he  had  a  snflleienl  number  of  instances  collected  to 
warrent  the  inference  that,  all  islands  sire  surround<Ml  by  water;  yet  Arch- 
bishop Wlialely's  concepi  ion  of  induction  does  not  rise  higher  than  this. 
The  Archbishop  agrees  with  Aldrick,  that,  from  the  examination  of  this  and 
that  magnet,  we  conclude  that  all  magnets  attract  iron;  when  in  truth,  mag- 
netism, the  quality  of  attracting  iron,  is  the  sine  qua  non  of  magnets,  and  it 
must  of  necessity  exist  in  every  thing,  which  may  be  called  a  magnet.  And 
we  discent  altwgether  from  :Mr.  Mills  definition  that,  "induction  may  be  con- 
sidered the  operation  of  discoverina:  and  proving  general  propositions."  And 
instead  of  believing  with  Mr.  Mill,  that   induction  is  at  the  foundation  of  all 


8 

general  propositions,  wd  do  not  think  that  any  general  proposition  can  be  ^ 
established  by  induction.    We  therefore  state  to  the  reader  that   the  process, 
about  which  we   shall   speak   hereafter   under  the   name  of  inductive,   has 
nothing  to  do  with  establishing  general  propositions,  and   that  s»ch   notion 
has  a  tendency  to  obscure  the  whole  subject. 

We  must  also  be  careful  to  avoid  another  error  ot  Mr.  Mill,  in  con- 
sidering induction  to  be  generalization  from  experience.  We  have  heretofore 
shown  that,  generalizatioM  from  experience  proceeds  upon  the  singular 
syllogistic  process;  and  if  we  go  any  farther  than  experience  and  infer  that 
cases  to  which  mankind's  experience  does  not  extend,  will  besiinilla  of  those 
falling  within  that  experience,  the  experience  is  not  an  inductive,  but  a  pro- 
bable one.  The  case  given  by  Mr.  Mill  himself  ot  the  mistake  made  by 
mankind  in  infering  that  all  swans  are  white  because  they  had  seen  a  great 
number  of  white  swans,  and  not  a  single  instance  of  a  swan  of  any  other 
color,  shows  that  Ihe  induction,  if  it  be  called  so,  was  faulty,  and  in  our 
estimation  it  was  no  induction  at  all,  but  merely  a  probable  inference  from 
numbers,  the  inductio  per  enumerationem  simplicem  of  Bacon.  Propable 
inferences  may  be  drawn,  with  which  we  are  perfectly  satisfitid,  though  we 
can  not  know  that  they  are  certainly  true.  Day  and  night  have  succeeded 
each  other  with  perfect  regularity  so  far  as  the  experience  of  mankind  ex- 
tends, and  for  that  reason  alone  there  is  a  strong  probability  if  we  can  see  no 
cause  for  a  change  thai  such  will  be  the  case  hereafter.  But  from  the  circum- 
stances that  no  exception  to  a  certain  uniformity  has  fallen  within  the  ex- 
perience of  mankind,  we  do  not  infer  by  the  inductive  process  that  there 
will  be  no  exception  hereafter.  From  the  continuous  uniformity,  extending 
through  experience,  we  are  led  to  believe  upon  the  ground  of  probability 
that  the  causes  producing  such  uniformity  will  continue  to  act  without 
interruption,  though  we  know  not  what  these  causes  are,  nor  that  they  will 
eertuinly  continue  uninterrupted 

The  case  of  the  naturalist  Inferring  that  all  horned  animals  are  cloven 
footed,  because  all  those  horned  animals,  which  have  fallen  within  the  ex- 
perience of  mankind,  are  so,  rests  entirely  upon  probabilities,  and  not  up<m 
induction  unless  the  inductio  purenumerationem  simplicem  be  true  induction. 
If  it  had  always  happened  within  our  experience  that  every  Friday  brought 
some  ill-luck,  the  inference  thai  every  Friday  in  the  future  will  be  unlucky, 
would  be  just  as  probable  to  our  minds  as  the  ca.sc  of  animals  with  horns 
having  cloven  feet,  yet  there  is  nothing  in  the  nature  of  such  inference  that 
corresponds  to  what  we  meon  by  induction. 

Again,  we  do  not  agree  with  Mr.  Mill  in  the  office  of  induction  in 
ascertaining  the  distance  from  the  earth  to  the  moon.  Mr.  Mill  says,  "the 
share  whidh  direct  observation  had  in  the  work  consisted  in  ascertaining  at 
one  and  the  same  instant,  the  zenith  distances  of  the  moon,  as  seen  from  tw« 


1  oints  very  remote  from  one  another  on  the  earth's  surface.  The  ascertain- 
ment of  these  angular  distances  ascertained  thtir  supplements;  and  since  the 
angle  at  the  earth's  centre  subtended  by  the  distance  between  the  two  places 
of  observation  was  deducable  by  sperical  trigonometry  from  the  latitude  and 
longitude  of  those  places,  tke  angle  at  the  moon  subtended  by  the  same  line 
became  the  fourth  angle  of  a  quadrilateral  of  which  the  other  three  angles 
were  known.  The  four  angles  being  thus  ascertained,  and  two  sides  of  the 
quadrelateral  being  radii  ot  the  earth;  the  two  remaining  sides  and  the 
diagonal,  or  in  other  words,  the  moon's  distance  from  the  two  places  of  ob- 
serration  and  from  the  center  ot  the  earth,  could  be  ascertained,  at  least  In 
terms  of  the  earth's  radius,  from  elementary  theories  of  geometry.  At  each 
step  in  this  demonstration  we  take  in  a  new  induction  represented  in  the 
aggregate  of  its  results,  by  a  general  proposition."  Now  we  do  not  c«insider 
that  thjrehas  been  any  induction  at  all  in  the  above  problem,  but  that,  after 
the  observations  are  made,  the  whole  process  is  syllogestic;  and  anyone,  who 
has  mastered  what  we  have  said  heretofore  in  Book  1st,  we  apprehend,  can 
make  the  application  and  demonstrate  the  problem  by  the  syllogism. 

Neither  do  we.agree  with  Mr.  Mill  that  the  uniformity  in  the  course 
of  nature,  or  what  is  the  same  thing  more  dttinilely  expressed  thai  like 
causes  with  like  conditions  will  produce  like  eflects  in  any  place  at  any  frime 
IS  the  highest  induction,  nor  do  we  consider  it  to  be  auv  inducii(;n  at  all. 
Neither  do  we  consider  "this  assumption,"  to  be  as  an  assumption  involved 
in  any  case  of  induction;  nor  can  we  consult  the  actual  course  of  nature  in 
this  regard  any  farther  than  our  experience  extends,  which  is  not  sufficient 
to  warrant  an  inductive  influence.  But  we  have  shown  heretofore  that  the 
unihumityof  nature,  or  that  like  causes  with  like  conditions  will  produce 
like  effects  in  aay  place  at  any  time,  is  demonstrated  to  our  minds  by  the 
plural  homonical  syllogism. 

There  in  a_n  other  improper  use  of  the  term,  induction  well  pointed 
out  by  Mr.  Mill,  it  is  the  case  of  the  navigator  approaching  land  and  bein- 
at  first  unable  to  determine  whether  it  be  a  comiuent  or  an  island;  but  afte" 
havmg coasted  around  and  having  arrived  at  the  same  point  from  which  he 
started  he  pronounces  it  to  be  an  island.  This  navigator  by  connecting  to- 
g(  ther  all  his  observations  finds  that  this  land  is  suriounded  by  water  and 
every  island  is  a  portion  of  land  surrounded  by  water,  and  iherefore'  this 
land  and  Inlands  are  similia-this  land  is  AN  island.  Mr  Mill  continues  to 
show  that  Kepler  ascertained  the  figure  of  the  orbit  travelled  by  the  planet 
Mars,  by  ob.servations  separately  made  but  connected  together  in  a  like 
manner  wiih  the  navigator,  and  justly  coiuludes  that  there  was  no  induction 
in  the  process  But  Mr.  Mill  considers  that  Kepler  did  make  one  inductive 
inference,  when  he  inferred  that  th«  planet  would  continue  lo  revolve  in  an 
elipse.      Now  if  this  inference  was  made  upon  the  grounds  that  like  causes 


9 

will  produce  like  effects  then  the  inference  was  syllogistic;  but  if  it  was 
made  upon  the  gr«»nnds  that  the  planet  had  always  gone  in  an  ellipse  hereto, 
fore,  the  inference  was  a  probable  one;  and  in  no  case  could  such  inference 
be  made  by  induction.  "^ 

These  remarks-might  be  continued  at  great  length;  but  if  the  student 
has  mastered  the  syllogism,  he  will  be  able  to  see  that  many  results  purely 
syllogistic  have  been  attributed  by  authors  to  induction,  and  that  the  term 
induction  is  very  often  used  without  any  definite  meaning  at  all.  Having, 
therefore,  ^t  the  mind  of  the  reader  free,  as  we  hope,  so  that  he  will  not  look 
in  wrong  directions,  we  will  proceed  and  come  nearer  to  the  subject,  and  ex- 
plain what  we  consider  to  be  true  induction. 

CHAPTER  II. 

INDUCTION  DISTINOUISIIED. 

Havins  spoken  in  the  previous  chapter  of  certain  notions  of  induction 
which  we  wish  the  reader  to  keep  out  rtf  his  mind,  while  following  us  in 
our  future  inquirers,  it  seems  necessary  now  to  state  what  we  mean  by  induc- 
tion, as  well  as  words  can  express  our  meaning  in  brief,  and  to  give  the 
reader  some  elue  to  the  directions  in  which  we  propose  to  go  in  search  oT 
truth  Induction,  then,  is  the  result  of  those  processes  of  the  mind  bv  which 
the  unknown  causes  of  any  given  effect  are  discovered;  and  the  processes  of 
the  min:l  engaged  in  such  discovenesare  the  inductive  processes.  We  stated 
in  a  former  chapter  that  we  gain  our  knowledge  of  cause,  in  the  first  ins- 
tance, through  effect,  i.  e.,  we  can  not  look  upon  any  agirregate  existence, 
and  before  we  have  the  knowledge  of  offects,  determine  such  existence  to  be 
or  lo  contain  a  potential  cause  of  any  given  effect.  And  in  studying  the  in. 
ductive  ]iroCesses  we  must  always  have  seme  given  effect  before  our  mind 
and  from  it  determine  the  eansos:  the  inductive  processes  have  nothing  to 
do  fn  taking  causes  and  from  them  determining  effects.  If  indeed  we  take 
two  elementary  substances  and  put  them  together  and  a  certain  effect  follow 
we  take  this  effect  and  determine  that  those  elementary  substances  :Were  the 
causes  of  it;  and  when  we  have  done  so,  we  have  also^  from  the  correlative 
natures  ol  cause  and  effect,  determined  that  the  phenomenon  which  we  call 
an  effect,  is  the  effect  of  those  causes;  but  we  must  always  keep  the  effect  in 
view,  it  must  he  in  view  always  before  the  inductive  processes  can  have  any 
thiuj^  upon  which  to  operate,  while  the  causes  of  a  given  effect  may  be  and 
alwavs  are  entirely  <Hit  of  siffht  or  without  our  knowledge  when  the  indue- 
tive  processes  commence  to  search  for  them.  If  th3  reader  will  bear  this  in 
mind  it  will  free  the  subject  from  much  obscurity,  which  otherwise  sur- 
rounds it. 

And  since  cause  and  effect  are  always  involved  by  the  inductive  pro- 
cesses, it  is  necessary  also,  to  put  flic  reader  Ujxin  his  guard  that  he  may  not 


cootoand  wbat  are  called  a  priori  and  a  posteriori  reasonings  with  indac- 
tioo.  After  that  we  hare  gained  the  knowledge  of  certain  effects  and  their 
causes,  we  look  upon  these  causes  and  their  conditions,  and  infer,  by  the 
plural  homonical  syllogism,  what  effects  will  follow,  without  waiting  to 
witness  such  effects  by  our  senses.  For  instance.  If  a  cannon  be  loaded  with 
dry  powder  and  a  man  be  about  to  apply  a  match  to  it,  by  the  plural  homoni- 
cal syllogism  we  infer  that  there  will  be  an  explosion  This  application  of 
the  syllogism  when  we  have  the  conditions  as  the  homopical  similia  or 
differentia,  whose  effects  we  know  in  the  premises,  and  from  them  we  infer 
the  effects  of  similical  similia  or  differentia,  whose  effects  hare  not  yet 
transpired  in  time  and  space,  is  called  a  priori  reasoning,  or  reasoning  from 
cause  to  effect    Induction,  however,  has  nothing  to  do  with  it. 

On  the  other  hand,  if  we  see  a  cannon  and  hear  the  report  of  its  dis- 
charge and  we  be  asked,  what  is  the  cause  of  this  report,  from  our  former 
knowledge  of  such  effect  and  its  causes,  by  the  plural  homonical  syllogism, 
we  infer  the  cause  of  thit  particular  effect.  And  this  application  of  the 
syllogism,  when  we  have  an  effect  whose  causes  and  conditions  we  know  as 
the  h«monical  homon  in  the  premises,  and  we  infer  the  causes  and  condi- 
tions of  a  similical  homon,  whose  causes  and  conditions  are  not  witnessed  by 
our  seos«a,  is  called  a  posteriori  reasoning,  or  reasoaing  from  affect  to  cause. 
But  there  is  n«  induction  in  it. 

Both  A  PRIORI  and  a  posteriori  reasonings  are  entirely  syllogistic.  In 
both,  some  particular  case  has  brought  by  induction  the  knowledge,  in  the 
ilrst  instance,  of  a  certain  effect  and  the  causes  and  conditions  of  it  to  our 
minds,  and  then  this  case  furnishes  the  premises  for  the  plural  homonical 
syllogism  to  work  with,  either  a  priori  or  a  posteriori.  But  when  the 
causes  of  an  effect,  an  homonical  homon,  are  unknown,  no  inference  can  be 
drawn  a  posteriori  respecting  thp  causes  of  a  similical  homon;  neither  can 
any  inference  be  made  a  priori  respecting  the  effect  of  similical  similia  or 
defferentia,  when  the  effect  of  homonical  similia  or  differentia,  the  effect  of 
such  causes,  is  unknown  to  us.  The  knowledge  of  certain  effects  with  their 
onuses  is  already  in  the  mind  before  a  posteriori  or  a  priori  reasonings 
begins.  The  inductive  processes  take  hold  of  any  given  effect,  the  causes  ot 
any  similical  effect  and  also  of  this  given  efl'ect  being  without  our  knowl- 
edge, and  search  out  and  induct  the  conditions  and  causes  of  the  given  effect. 
Keeping,  then,  iu  mind  that,  a  priori  and  a  posteriori  reasoning  are  syllo- 
giatic  and  that  they  proceed  kom  certain  known  cases  to  infer  respecting 
similical  cases,  while  the  inductive  proces«es  proceed  from  a  given  phenome- 
non to  make  knoxn  to  us  the  causes  and  conditions  qf  that  phenomenon,  we 
will  proceed  farther,  hoping  that  we  will  not  be  misunderstood 

Now  in  speakinc  of  cause  and  effect,  it  is  usual  ^iih  philosophers  to 
cull   the  cause  au    antecedent  and  the  effect  the  consequent.    These  terms, 


antecedent  and  consequent,  have  reference  to  the  relations  of  pel  its  In  time, 
and  we  have  already  shown  heretofore,  that  time  possesses  no  capatial  gre- 
garia  and  that  it  can  not  be  the  cause  ,of  any  changa  or  effect.  And  therefore 
if  we  say  that  a  cause  is  an  antecedent,  wt  must  mean  only  that  the  existence 
whatever  it  may  be,  to  which  we  refer  as  cause,  occupied  a  point  in  time 
prior  to  the  point  occupied  by  the  existence  which  we  call  the  effect.  And 
although  this  be  true,  yet  it  does  not  with  any  deflniteness  determine  a  cause. 
If  we  say  that  a  cause  is  an|antercedent  of  an  effect,  i.  e.,  a  cause  and  an  an- 
tecedent are  homon,  we  may  still  enquire  what  antecedent  is  referred  to  as 
connected  with  any  given  effect,  for  there  are  many  things  which  existed  \m 
nature  prior  to  John  Smith's  being  intoxicated,  and  which  antecedent  Is 
connected  with  this  effect?  It  is,  therefare,  merely  the  condition  of  a  cause 
that  it  exist  antecedently  to  an  effect;  but  antecedent  is  a  term  which  can 
not  be  used  as  synonomous  with  cause. 

Now  we  have  shown  heretofore  that  time  and  space  can  not  be  the 
causes  of  any  thing ;  they  are  however  tha  conditions  of  all  causes  and  effects, 
and  they  are  the  only  things  of  which  we  shall  speak  in  our  future  inquiries 
as  conditions.  Every  thing  in  nature  which  can  be  a  cause,  can  be  cause 
only  upon  the  conditions  of  time  and  space,  and  that  which  has  once  been  a 
cause,  will  in  like  conditions  of  time  and  space  in  the  future  be  a  cause  again. 
A  condition  which  presents  the  absence  of  a  preventing  cause  is  sometimes 
confounded  with  a  cause,  as  the  absence  of  the  air  in  a  pump  is,  sometimes 
said  to  b«  the  cause  of  the  water  rising  in  it.  This  however  is  but  a  condi- 
tion of  space. 

We  define  causes  therefore,  to  be  thecapacial  gregaria  of  the  aggregate 
existences  from  which  gieen  changes  or  effects  spring.  To  go  behind  the 
eapacial  gregaria  of  aggregate  existences  and  inquire  into  the  ontology  of 
these  eapacial  gregaria  is  no  part  of  our  undertaking  at  present.  We  may 
say,  indeed,  that  they  are  the  maifestations  af  the  Deity's  will,  i.  e,.  that  they 
are  the  eapacial  gregaria  of  the  Almighty  himself  made  tanirable  to  us;  but 
we  take  these  eapacial  gregaria  of  existences  made  known  to  us,  as  the  only 
causes  of  which  we  shall  treat  and  we  shall  regard  them  as  the  primary 
causes  of  all  the  effecU  in  nature.  If  any  one  shall  say  that  the  Almighty  is 
still  a  priar  cause,  we  have  no  objection. 

t  And  it  will  occur  to  almost  any  ona,  after  what  has  been  said  about 
cause  and  effect  in  a  previous  chapter,  that  an  homonical  eapacial  gregarium 
per  se  can  not  be  a  cause  of  any  given  effect;  there  must  be  heterical  gregaria 
implicated  before  any  effect  can  be  produced.  If  we  take  an  ivory  ball, 
whiQh  poasesses  the  eapacial  gregarium  of  impenitrability,  i.  e.,  the  power 
to  r«»ain  in  space,  we  must  see  that  this  eapacial  gregarium  per  se  can  pro- 
doe*  DO  effect  whatever.  If  the  ball  be  at  rest  iU  impenitrability  can  not 
Start  it.  and  if  it  be  in  motion  its  impenitrability  can  not  stop  it;  the  impeni 


8 

ir  .bility  in  the  ball  can  per  sc  produce  nothing.  But  if  an  other  ball  pos- 
^i'-ssiag  also  impentrability  be  brought  to  bear  uponlhc  first  one,  the  heterical 
impenilrabriities,  ouj  in  each  ball,  can  inter  se  produce  an  effect.  Homon 
per  se  must  always  remain  homon,  and  per  se  no  effect  can  spring  from  an 
homouical  gregarium;  and  hence  all  effects  in  nature  are  produced,  not  by  an 
homonical  gregaridm,  but  by  heterical  gregaria.  And  as  the  capacial  gre- 
gariaof  the  aggregate  existences,  from  which  changes  spring,  are  the  causes 
of  all  the  phenomena  of  nature,  it  is  necessary  in  seeking  for  these  causal 
gregariaof.auy  effect,  to  find,  in  the  first  place,  the  aggregate  existences 
possessing  the  said  gregaria,  and  to  seperale  them  from  others. 

And  in  contemplating  the  aggregate  existences,  \yhose  capacial  grega- 
ria are  causes,  it  will  readily  appear.lhai  aggregate  exlstenc?s  may  be  divided 
into  primary,  secondary,  tertiary  and  quartuary  aggregations!    By  a  primary 
aggregate  existence    then,    we  mean   what   is  usually  called    an    elementary 
substance,  and  by  secondary  aggregations,   those  substances  compounded  of 
two   elements,  by  tertiary    aggregations,    substances   compounded   of  three 
elements,  if  such  compounds  exist  in  nature,  and  so  on.     And  if  we  take  any 
primary  aggregate  existance,  a  jar  of  oxygen  for  instance,  as  this  is  an  ele- 
mentary thing,  it  contains  all  the  capacial  gregaria  of  any  oxy^^en.     For  if 
any  other  o.xygeu  can  be  found  with  a  less  number  of  capacial  gregaria,  then 
the  first  jar  was  not  elementary.     But  if  we  examine  any  el(?mcnlary  oxygen, 
a^  all  other  o.xygen  is  a  simile  of  that  whicli  we  have  examined,  any  experi- 
ment with  certain  oxygen  giving  a  certain  result  will  under   like  conditions 
give  a  simile  of  that   result   with  any   oxyjren;   and  so   also  »vith  any   other 
priniary  ajrgregate  existence.    And    the   differential  elements  constitute  the 
primary  aggregate  existences  in  which    reside  the  capacial   gregaria   which 
arejhe. primary  causes  of  all  effects  in  nature.     These  elements  combine  and 
^"'i^Nvl'.V*'"'^'^' ^*^"M^"iin^J9,   which  possess  capacial    gregaria   different   from 
those  possessed  by  eit^jer  of  the  elements  entering  into  th«m. 

.     Now  every  capacial  gregarium    ]  ossessed  by  a  primary  aggregate  ex- 
istence, is  a  sine  qua  non  of  that  aggregation,  and  it  has  a  simile  of  itself  in 
every  other  aggregate  existence,  which  is  a  simile  of  the  given  aggregation; 
and  this  is  true  also  of  all   compounds.     And  hence  we  can  experiment  upon 
all  aggregate  existances,  and   by   the  homonical    syllogism,    infer   from   the 
result  in  any  case  the  results  in  all  cases   of  similical  similia   or  differentia, 
xlnd  the  first  things  to. be   determine;!   by  observation    or    experiment, 
about  aggrcirate  existences,   are  the  conditions  of  time  and   space  by  which 
their  capacial  gregaria  are  regulated.    And  if  we  find   by    observation  or 
experiments  upon  nature  that,  a  certain  gregarium  of  a  certain    asTgregation 
is  conditioned  in  a  certaiR  manner,  we  know  that  a  sniiLE  of  that  gregarium 
in  similar  au;gregations,  will  be  conditioned  ia  a  similia  manner,  and  in  like 
mauiiLr  and  with  like'  iii'ereuces,  wj  may   experiment  with   the  gregaria  in 


9 

fasciculo,  with  aggregate  existences  themselves.  Having  now  cleared  the 
way,  as  we  hope,  we  will  in  the  next  chapter  proceed  to  explain  the  conditions 
of  time  and  space,  which  regulate  the  causal  gregaria,  and  we  will  then  see 
the  manner  of  proceeding  to  soihc  extent,  and  the  reader  will  be  able  to  un- 
derstand better,  what  we  mean  by  induction. 

CHAPTEK  III. 

CONDITIONS  OF  TIME  AND  SPACE. 

We  have  already  said  that  the  conditions  of  causes  and  effcctsaretime 
and  space;  we  have  also  shown,  that  not  an  homonical  gregariam  but  heter- 
cal  gregaria  are  the  causes  of  every  effect.  And  in  a  previous  chapter  upon 
cause  and  effect  we  showed  tliat,  in  every  effect  some  homon  becomes  hetera 
or  some  hetera  becomes  homon,  some  similia  become  differentia  or  some 
differentia  become  similia,  some  commensura  become  incoraensnra  or  vice 
versa;  this,  we  saw,  is  a  condi,tiou  of  causiition.  And  if  we  take  two  ivory 
bali-^,  dich  of  which  possesses  impenitrability,  we  must  see  that  the  impeni- 
trabilities  of  the  balls  are  hetera  in  space;  but  we  must  see  also  that,  unless 
these  hetera  in  space  occupy  an  homonical  time,  i.  e.,  unless  their  times  be 
homon,  no  effect  can  be  pr(»duced  by  ihem  inter  se.  If  an  effect  is  to  be  pro- 
at  a  certain  point  of  time  between  two  ivory  balls,  but  before  that  point  of 
time  come,  one  of  the  balls  be  annihilated,  we  must  see  that  the  proposed 
effect  can  nt)t  tratispire  from  the  want  of  an  homonical  time  for  the  two  balls. 
Those  existences,  which  existed  yesterdiy  but  not  to-day,  can  not  be  the 
causes  of  effects,  which  begi  i  to  transpire  to-day,  i.  e.,  causes  must  possess 
an  homonical  time  witli  that  point  in  which  the  effect  begins  to  transpire  or 
originates.  And  lience  let  the  effect  be  the  removal  of  a  cart  from  a  certaia 
place  to  another  upon  a  hill,  and  let  us  take.it  for  granted  that  some  horse 
<lrew  the  cart  up  the  hill,  and  suppose  we  wish  to  ascertain  the  individual 
horse  that  did  it.  In  the  first  place  we  must  ascertain  the  homonical  time  in 
which  this  effect  occurred,  then  we  may  think  of  Bucephalus  the  horse  of 
Alexander;  but  we  know  that  he  could  not  have  done  it,  if  the  times  of 
Bucephalus  and  of  the  effect  arc  hetera.  And  we  know  that  no  other  horse 
than  one,  whose  time  of  existence  is  homonical  with  the  time  of  the  effect, 
could  have  done  it.  But  anv  horse,  whose  time  is  homonical  with  that  of  the 
effect,  may  have  done  it,  i.  e.,  such  horse  fulfills  the  condition  of  time.  And 
hence  all  aggregate  existences  possessing  the  causal  gregaria  of  any  given 
effect,  must  be  synchronous  with  the  transpiration  of  tlw  effect,  i.  e.,  their 
times  and  the  time  of  the  beginning  of  the  effect  must  be  homon. 

Let  us  next  look  into  the  conditions  of  space.  For,  as  all  the  acting 
causes  of  any  given  effect  must  be  synchronous  and  in  space,  we  m?^st  deter- 
mine the  conditions  of  space;  and  where  the  conditions  of  space  can  be  de- 
termined, we  know  that,  no  aggregate  existence,  outside  of  those  conditions 


10 
in  any  given  case,  can  be  an  aggregation,  which  contains  tlie  causal  gregaria 
or  a  causal  gregarium  of  the  given  effect.  Aud  we  must  remark  that,  where 
two  aggregate  existences  contain  the  heterical  gregaria,  which  are  the  causes 
of  any  given  effect,  these  gregaria  must  operate  through  the  space  situated 
between  the  two  aggregations. 

A B 

If  A  and  B  be  two  aggregate  existences  with  a  certain  space  between 
them,  and  A  put  forth  certain  energies,  these  energies  must  take  some  direc- 
tion in  space;  and  unless  they  take  the  direction  towards  B,  the  energies  of 
A  and  B  can  not  meet  in  an  homonical  where,  and  unless  the  lufterical  ener- 
gies come  to  an  homonical  where,  no  effect  can  follow. 

D A B C 

Suppose,  for  instance,  that  the  encgies  of  A  take  ihe  direction  only 
towards  D,  and  the  energies  of  B  only  towards  C,  then  the  spaces  of  these 
heterical  energies  will  always  remain  hetcra,  and  no  effect  can  follow  from 
ti»ese  heterical  energies  inter  se.  The  conditions  of  agi^regite  exiMtenees  in 
space,  therefore,  necessary  to  causation,  are  thai,  the  helerioil  gregaria  pos- 
sessing heterical  wheres,  shall  find  an  homonical  where,  i.e., that  their  wheres 
shall  in  some  point  of  space  come  to  b«;  homon.  And  it  will  readily  l)e  sug- 
gested that,  though  these  energies  may  take  the  direction  towards  each  other, 
yet  they  may  not  meet. 


C- 


-D 


B 


Thus:  Suppose  A  to  be  a  niitgnet  and  B  an  iron  filing,  if  A's  energies 
terminate  at  C  and  B'j  at  D,  then  they  have  n  )t  tound  an  homonical  where, 
and  therefore  no  effect  can  fallow. 

Now  a  homon  of  time  and  a  homon  of  space  are  the  conditions  sine 
quibus  non  of  causation;  and  all  the  gregaria,  which  can  be  causes.,  must 
come  into  these  two  homonical  hetera.  And  hence  whenever  any  effect 
takes  place,  these  conditions  have  been  fulfilled;  and  the  object  of  inductive 
inquiry  is  to  find,  not  only  what  objects  fulfill  thebe  conditions,  but  also  what 
objects  operate,  become  acting  causes  in  these  conditions,  i.  e.,  what  gregaria 
in  these  conditions  are  the  sine  quibus  non  of  any  given  eftect.  And  we 
must  always  recollect  that,  we  must  have  a  certain  effect  in  view,  and  that 
effects  inter  se  similia  may  be  produced  by  sets  of  causes,  inter  se  similia,  i.e., 
by  similical  similia  or  similical  differentia.  And  »i.s  gregaria  are  found  in 
aggregations,  we  must  first  determine  the  aggregations  containing  the  causal 
gregaria  of  any  given  effect  to  this  task  we  will  tow  proceed. 

CHAPTEK  IV. 

HETERICAL  INDUCTION. 

We  have  heretofore  treated  of  simple  heteration  and  shown  that  Ihe 
power  of  the  mind  to  heterate  depends  upon  time  and  space.    The  succession 


U 

lof  our  own  thoughts  in  time  enables  us  to  heterate  them,  and  the  revolution 
lof  the  ewth  and  of  the  heavenly  bodies  in   time  enables  us  to  fix  upon  any 
'particular  i>eriod  of  time  and  hold   its  relations  in  our  miud.    By  the  where 
[of  ourselves  and  the  where  of  other  objects  in  space  and  their  relations  inter 
I  se  we  are  also  enabled  to  locate  a  particular  where  in  space   and  preserve  its 
relations  in  our  minds.    And  although  we  may  not  always  be  able  to  point 
out  the  precise  point  of  time,  in  which  a  given  eftect  begins  to  take  place,  we 
can  generally  come   near  enough  to  that  period  fi)r  the  purposes  of  heterical 
induction;  and  so  also  we  can  come  sufticiently  near  to  the  precise  where  in 
space  of  a  given  eftect.    Simple  heteration   is  sufficient  to  bring  us  to  the 
poMil  ot  time  and  the  point  of  space  of  any  given  effect  i  nder  consideration 
of  tl»e  inductive  processes.    And  when  we  have  the  period  of  lime  in  which 
any  given  eftect  took  place,  as  the  cause  of  that  effect  must  have  been   inter 
se  synchronous  and  have  touched  upon  some  homonical  point  of  that  period 
of  time,  no  aggregations  before  or  since  that  period  could  contain  the  causal 
gregaria  of  that  effect.    If  the  .Enead  was  written  in  the  age  of  Augustus, 
no  person,  who  lived  and  died  before  that  age,  or  who  has  been  born  since, 
could  have  written  it.    And  hence  if  we  know  the  period  of  time  in  which 
any  given  effect  took  place,  all  aggregate  existence,  which  have  not  an  ho- 
nionrcal  time  with  that  period,  are  immediately  heterated  from  the  causes  of 
the  effect  by  our  minds;  and  this  is  heterical  induction.    For,  when  we  have 
tlu<.wn  out'those  exisfmces,  which  could  not  have  been  the  causes,  we  have 
before  us  other  existences,   which  may  hare  been  the   causes,  and   by  casting 
out  the  former  we  have  led  in  or  inducted  the  latter.    And  were  there  but 
two  ag-regate  existences  in  esse  at  the   period  of  time  of  the  effect,  as  there 
must  have  been  heterical  gregaria  concerned  in  producing  it,  we  would  know 
by  the  heterical  inducti.m  of  aggiegations  by  their  times  alone  that,  these 
two  existences  contained  the  causal  gregaria  of  the  effect. 

But  although  the  heteration  of  objects  from  the  time  in  which  any 
given  effcHJt  takes  place,  by  throwing  out  many  aggiegations  which  could  not 
contain  causes  of  the  effect,  narrow  the  field  in  which  the  causes  are  to  be 
found.  Yet  there  are  afterwards  so  many  aggregate  existences  in  esse 
synchronous  inter  se  and  having  times  homonical  with  that  of  the  eftect, 
and  any  of  which,  therefore,  so  far  as  time  is  concerned,  may  have  been 
causes  of  the  effect,  that  after  that  we  have  determined  the  hom  »jiical  timeof 
the  effect  and  determine  also  what  existences  have  limes  homonical  with 
this,  we  are  still  unable  to  tell  which  of  these  contemporary  existences  con- 
tained acting  causes  in  the  present  instance.  We  have,  therefore,  to  proceed 
farther  and  heterate  the  wheres  ot  objects  from  the  homonical  where  in 
which  the  effect  took  place.  Although  this  be  an  easy  matter  in  s  >me  n  - 
stances,  vet  in  olh-rs  it  is  attended  with  great  difficulties.  If  we  f^eci  an  ob- 
ject in  motion  by  heterical  impenetrabilities,  if  a  ball  be  started  by  the  impact 


12 

of  some  other  objecf,  every  object,  wliichal  llie  homonical  vime  of  theeffeci's 
beginning,  was  outside  of  the  honionical  where  of  impact,  i.  e.,  whose  where 
and  the  where  of  impact  were  hetera,  can  be  immediately  heterated  by  the 
mind  from  the  causes  of  the  effect.  And  so  also,  from  the  very  nature  of 
compounds,  we  know  that,  the  iuirredients  compounded  must  come  in  contact 
or  tliey  wt.uld  not  enter  into  compounds  together. 

And  aiihogh  we  can  not  tell  but   that   other  existences  than   those  in- 
gredients which  enter  into  compounds,  may  havo  something   to  do  with   ihe 
compounding  of  those  ingredients,  yet  if  the  action  of  these  other  existences 
be  always  constant  at  all  times  and   places,  whenever  and   wherever  a  given 
effect  IS  offereJ  to  our  senses,  for  all  practical   purpose**  their  action  mnv  be 
omitted  in  our  considerations  without  any  error  to  our  principle*  or  results. 
Thus;  although  we  may  nor  be  able  I  .  het.-rate  tlio  space,  which  bounds  and 
limits  the  capaciai  gregaria  of  the  n.>rtli  polar  star,  from  the  spacu-  in  whieh 
pine  sh.svings  are  burning,  yet  if  the  influenee  of  t  .e   n.irth  star  be  constant 
whenever  and  wherever  shivirigs  and   tire   are  found    upon  our  earth,  for  nil 
practical  purposes  we  may  omit  this  inttiience  in  our  considerations Mud  s,ek 
after   other   nggregafi  >ns,  whose  capaciai    gregaria  we    can    delcrnnnc   and 
limit  in  space;  and  if  their  space  and  the  space  in  which  shavinirs  are  burn 
ing  be  hetera,  wo  may  immediately  heterate  those  other  agirngatins  from  the 
causes  of    the   effect.     And  hence,  wlienever,  for  instance,  we'' find    soap,  we 
feel  assured  that  no  ingredients  outside  ot  those  which  hav,.  eome  in  contact, 
can  c.ntain  the  causes  of  soap,  or  at  least  we  may  look  for  and  receive  a^ 
causes,  if  not  all  of  the  cau^^es,  scmie  capicial  s^regaria  conlaineu  in  the  in- 
gredients, which  have  come  in  contact   when  soap  came  into  existence  as  an 
effect. 

But  in  numerous  instances,  for  the  purposes  ot  the  hefeiical  induction 
of  aggregations  in  space,  we  must  follow  Bacon's  rule  of  varying  the  circum- 
stances, i.  e.,  we  must  find  what  capaciai  gregaria  of  aggregate  e'xistences  are 
within  the  homonical  time  and  place  of  given  effects  in  one  and  the  other  in- 
stance of  similical  effects.     Sometimes  by  observation  upon  numerous  instan  - 
ces  of  similical  effects  in  nature,  we  are  able  to  heterate  aggregate  existences 
from  others  containing  the  causal  gregaria ;  and  very  frequently  we  can  do  this 
by  experiment.     If,  in  the  consideration  of  compounds  for  instancy,  a  chemist 
can  analyse  and  find  a  certain  portion  of  water  to  contain  the  primary  aggre 
gallons,  oxygen,  hydrogen  and  sulphur,  in  one   inMance,  and  in  anothor  in- 
stance, he  find  a  j  ortion  of  water  to  ct>ntain  oxygen,  hydrogen  and  poiasium 
he  may  then,  by  the  latter  instance,  heterate  sulphur  from  the  sine  quibus  non 
of  water;  for,  in  the  latter  instance,  water  occurs  wiihout   sulphur   being   in 
the  homonical  space  of  the  effect:  and  by  the  former  instance  he  can  heterate 
potasium  from  the  sine  quibus  non  of  the  effect.     But    it  is    not   quite   clear 
from  the  above  analysis  of  the  chemist,  that  both  potasium   and  sulpliur  can 


l)t*  absent  from  the  water;  for,  oxygen  and  hydrogen  may  not  unite,  for  any- 
ihiijg  we  yet  know,  into  the  c(im,)ouud  of  water,  wiihout  the  presence  of 
riihor  tne  one  or  the  other  of  these  substances.  Hut  if  Ine  chemist  find  a 
l)()ilion  of  water  containing  only  oxygen  and  hydrogen,  he  may  liien  heterate 
all  (Jther  aggregations  IVoin  the  sine  quibus  non  ot  water.  15ul  neither  oxygen 
iinr  hydrogen  can  be  lieterate<l  from  the  causes;  for,  they  are,  each  of  them, 
primary  aggregations,  and  were  one  ol  them  taken  away,  there  would  not  be 
lell  lielerical  gregaria  lo  produce  an  eti'eel.  Now  ii  a  chemist  can  take  cer- 
lain  elements  ami  by  them  produce  aconipor.nd  or  any  given  result,  the  mode 
'  I"  making  heterical  iiidnclioijs  in  the  case  is  the  same  as  in  analysis.  He 
nuwl  wait  until  he  perceives  the  efVecl,  before  he  can  heterate  any  object  from 
:,.  causes  of  il.  'liie  only  dilference  is  that  in  analysis  he  must  seek  after 
'!(••  .girreiratlons,  wiiicii  are  in  the  homonical  lime  and  place  of  the  etlccL  in 
lilVer  nt  insiane.es,  while  in  synthesis  he  already  knovys  the  aggregations  ia 
ilie  homonical  lime  and  place  (»f  the  ellect  wiihout  inciuiriug  after  Ihcm. 

And  in  general,  if  we  suppose  any  given  effect,  lo  contain  in  its  hoiuoiu 
iial  lime  and  place,  Ihe  aggregations  represented  by  a,  li,  c  and  d,  in  one 
instajute,  ami  in  another  instane*'  a,  1),  c  t,  andin  slill  another  a,  b,  g,  h, 
we  may,  from  ihe  consideration  of  these  three  instances,  helerale  each  of  the 
iigreiralion?*  severally,  excepting  v  and  u,  iVojn  the  sine  quibus  non  of  the 
riitci:  Mionuh  it  is  not  certain  thil  a  and  n  alone  could  produce  the  effect 
wi'lm  II  ilif  jU'esenc  «'i'  --ome  of  ihe  others,  unless  we  can  tind  an  instance  in 
hich  they  alon»  ;ii,  present.  Bacon's  rule  of  varying  the  circumstances,  or 
.1  .  .aminiiu-:  ditferent  in-tanCi*sof  similical  elfects,  il  will  be  peiceivcd,  ena- 
!.i-  M<  to  heterate,  from  the  causes  in  certain  cases,  objects  occupying  the 
homonica'  time  and  space  of  an  etfecl;  onenastance  can  be  used  to  enable  us 
to  heterate  some  oi'  the  aggregations  from  the  sine  quibus  non  of  another. 
This  matter  of  varying  the  circumstances  and  thereby  gaining  the 
<lala  from  which  hete«ical  induction  can  proceed  may  be  explained  in  a  little 
(lifferent  manner  from  that  already  given,  though  il  comes  to  the  same  thing. 
Thus;  if  we  mix  t(»gether  three  gasses* represented  respeclively  by  a,  b,  and  c, 
:\ni\  we  apply  this  mixture  to  a  piece  of  while  paper,  for  inslauce,  and  ob- 
serve the  change  or  effect,  which  takes  place  in  the  paper,  an  1  we  then  apply 
Ihe  thne  jrasses,  a,  d  and  e,  and  observe  also  the  effect  upon  the  paper,  and 
we  find  the  two  ellecis  lo  be  inter  se  similia,  the  latter  instance  enables  us  to 
lu'terate  b  and  c  from  the  sine  quibus  non  of  such  similical  effects,  and  the 
lormer  instance  enables  us  to  heterate  d  and  e  trom  the  sine  quibus  non, 
leaving  the  effect  to  take  place  between  the  capaciai  gregaria  of  a  and  of  Ihe 
paper.  Il"  we  represent  the  paper  by  x,  we  may  say,  a,  b.  c  and  x  produce  a 
given  effect,  which  we  observe  upon  x,  but  a  similar  effect  is  produced  upon 
.\  by  a,  d,  e  and  x.  and  therefore,  b  and  c  are  not  sitic  quibus  non  ol"  such 
effects,  nor  Hie  d  and  e.     And  if  a,  b  and  c,  each  of  them,  leave  changes  upon 


14 

the  paper,  which  can  be  inter  se  discriminated,  which  changes  may  be  rep- 
sented  respectively  by  the  capitals  A,  B  and  C,  and  in  an  other  instance,  a,  d 
and  e,  produce  changes,  which  can  be  discriminated  inter  se,  we  may  then 
find  from  the  gregaria  of  a,  b,  c  and  x  the  eftecls  a,  b,  c,  and  from  the  gre- 
garia  of  a,  d,  e  and  x,  the  effects,  a,  d,  e,  and  from  these  data  we  can  heterate 
b  and  c,  and  d  and  e,  from  the  sine  quibus  non  of  the  eflect  a  &c. 

Heterical  inductions  are  made  daily  in  the  transactions  of  life  and  al- 
ways have  been  so  made,  though  like  the  syllogistic  process,  the  modus 
operandi  of  the  mind  has  not  been  well  und«rstood.  A  very  simple  case  of 
heterical  induction  is  continually  made  before  courts  of  law.  If  a  man  be 
indicted  for  murder  and  an  alibi  be  proven,  i.  e.,  if  it  be  clearly  shown,  tiiat 
the  person  charged  with  the  crime,  was  at  the  time  when  the  crime  was  com- 
mitted, a  hundred  miles  from  the  place  in  which  it  was  done,  the  accused  is 
heterated  from  the  causes  of  the  murdered  man's  death  The  principle  nf 
heterical  induction  may  be  summed  up  in  the  following  hetriical  i>r()posi- 
tion;  whatever  is  absent  from  the  homoiiical  time  or  i)lace  of  a  given  effect, 
and  the  causes  of  that  effect,  arc  hetera. 

CHAPTER  V. 

ITOMONICAL  INDITTION. 

In  the  previous  chapter  we  explained  the  modus  operandi  of  the  mind 
in  separating  those  aggregate  existences,  whose  gregaria  can  not  be  causes  of 
a  given  effect  from  other  aggregations,  whose  gregaria  may  be  the  causes  so 
far  as  time  and  space  are  concerned,  i.  o.,  their  times  and  wheres  fulfill  the 
conditions  of  causation.  In  the  present  chapter  we  must  show  the  process  of 
the  mind  in  determining  what  aggregations  fulfilling  the  conditions  of  time 
and  space,  and  the  aggregations  containing  the  causal  gregaria  are  homoni- 
cal  hetera.  Although  we  may  heterate  all  other  objects  from  the  homonical 
place  of  a  given  effect  at  the  time  the  efiect  took  place,  excepting  a,  b,  c,  yet 
it  is  not  certain  that  a,  b,  c,  each  of  them,  contain  the  causal  gregaria  of  the 
given  effect,  nor  is  it  certain  which  of  them  do  contain  causal  gregaria. 
Three  men  may  have  hold  of  a  rock  when  it  begins  to  move,  and  yet  one  of 
them  may  have  done  all  the  lifting.  And  supposing  that  lye,  sand,  sawdust 
and  adipose  tissue  be  put  together  in  a  kettle  and  boiled,  and  soap  be  the 
result,  which  of  these  ingredients  contained  the  causal  gregaria  of  the  effect? 
We  might,  no  doubt,  heterate  some  of  these  ingredients  from  the  causes  in 
the  manner  pointed  out  in  the  last  chapter,  but  our  object  now  is  not  to  find 
existences,  which  in  relation  to  the  causes  of  the  eflfeet  are  heterical,  but  to 
find  the  aggregations,  which  are  homonical  with  these  containing  the  causes. 
And  in  order  to  find  the  homonical  aggregptions  we  must  again  follow  Ba- 
con's rule  of  varying  the  circumstances  Suppose  we  take  lye,  sawdust  and 
sand  without  any  adipose  matter  and  boil  them  just  as  spoken  of  above,  and 


15    ■ 

find  that  no  soap  is  produced,  we  may  then  conclude  that  adipose  matter  was 
a  sine  qua  non  of  soap  in  the  first  experiment.  And  hence  when  we  wish  to 
ascertain  whether  any  one  of  the  aggregations,  fu'filling  the  condilionsof  the 
lime  and  place  of  a  given  efiect,  be  a  sine  qua  non  of  that  effect,  we  first  as- 
certain, if  possible,  all  the  aggregations  fulfilling' those  conditions,  and  then 
we  find  an  other  case  having  all  the  aggregations  as  before,  excepting  that 
aggregation,  whose  gregaria  as  sine  quibus  non,  we  wish  to  try;  and  if  in  the 
latter  caee  the  effect  is  not  produced  as  in  ihe  former  one,  then  this 
uiTJiregalion  left  out  of  the  latter  case  was  a  sine  qua  non  of  the 
effect  in  the  former  c.ise.  Thus;  if  in  one  case  we  find  the  aggrega- 
tions fulfilling  the  conditions  of  the  time  and  place  of  the  effect  a,  to  be 
a,  b,  c,  and  d,and  in  an  other  case  we  find  a,  b  and  c  without  d  in  like  condi- 
tions as  befo«'e,  without  the  effect  a,  we  then  have  the  data  from  which  to 
niake  the  houu)uical  induction,  that  d  was  a  sine  qua  non  of  a.  Tliat  the 
sun  is  a  sine  qua  non  of  day  may  be  proven  by  taking  the  case  of  a  bright 
(lay  and  a  case  in  the  same  day,  when  the  sun  is  eclipsed  by  the  interposition 
of  the  opaque  body  of  the  moon,  or  when  the  earth  ret^olves  and  takes  us 
away  from  the  sun. 

And  it  is  no  matter  which  of  the  tw<;  cases,  one  of  which  contains  all 
the  airffrejrations  and  Ihe  other  all  excepting  one,  come  under  our  observation 
first.  If  a,  b,  0  and  d,  be  found  in  ct;rlain  conditions,  and  then  e  also  come 
into  those  conditions  ajid  then  the  eflect  a  immediately  commence,  all  the 
data  of  tWe  two  eases  requirerl  are  furnished.  Before  the  sun  rises,  we  have 
the  aggregations,  a,  b,  c,  .  .p  without  day;  when  the  sun  rises  we  have  ihe 
aggregations  a,  b,  c  .  .p  and  the  sun,  and  then  it  is  day.  And  if  we  can  find 
cases  by  which  we  can  thus  try  successively  each  one  of  the  aggregations 
fulfilling  the  conditi(ms  of  time  and  space,  we  may  find,  by  homonical  in- 
duction, all  of  the  aggregations  containing  all  the  causal  gregaria  of  any 
given  effect.  But  we  must  be  sure  that  the  case,  in  which  the  effect  does  not  . 
occur,  contains  all  the  aggregations  excepting  the  one,  which  we  are  trying 
as  to  its  being  a  sine  qua  non,  and  which,  the  ease,  in  which  the  effect  fol- 
lows contains.  Thus;  if  the  case,  in  which  the  eflect  a,  follows,  contain  the 
aggregations,  a,  b,  c,  d  and  e  in  an  homonical  time  and  place,  and  we  wish  to 
see  whether  a,  was  a  sine  qua  non  of  that  eflect,  we  must  find  a  case  in  which 
1),  c,  d  and  e  are  found  in  a  similical  time  and  place  without  the  eflect. 

If  there  be  more  aggregations  in  the  case  in  which  the  efl'ect  does  not 
follow,  i,  e,  if  there  be  b,  c,  d,  e  and  f  in  the  case  without  the  effect  a,  and  a, 
h,  c,  d  and  e  without  f  in  the  case  where  the  eflect  follows,  as  the  effect  adoes 
not  follow  in  the  former  case,  the  additional  aggregation  f  vvouid  not  vitiate 
our  inference  respecting  as  being  a  sine  qua  non  in  the  latter  case,  unless 
some  effect  due  to  f  should  prevent  the  effect  a  in  the  former  case.  If  a,  b,  c, 
d  and  e  be  found  to  make  a  compound  in  the  condition  g,  and  b,  c,  d,  e  and  f 


M 


4 


16 

remain  but  a  mixluic  in  the  rondilion  g,  we  may  infer  a  to  luivc  been  a  sine 
«iua  non  in  the  former  case,  unless  f  he  a  pi  eventing  cause  in  tlie  latter  one. 
But  for  entire  certaint}^  it  i>;  neec^<jary  that  the  two  njisen  nvrvt'C  in  the  affgre- 
ffations  except  the  one  which/ve  arc  tiyini;.  If  we  have  a  niven  ettect  a, 
with  the  ag<,n"egaiions  a,  b,  c  an<l  d,  in  one  case,  and  in  an  other  case  we  have 
the  ag.2;regations  b  and  conly  and  without  tlie  etVeet,  we  can  not  tell  which  or 
whether  both  a  aud  d  were  not  sine  qwibns  non  «f  the  elteet  a,  in  the  formen 
case.  The  principle  of  honionical  induction  may  be  summed  up  in  the  fol- 
lowing homonieal  i)i()position  ;  whatever  existences  an'sin<'  quibus  non  in  the 
homonical  time  and  j)Iace  of  an  ellVet  and  the  .iin^i!  livj-iiI  i  of  th.ii  .;:,.!, 
are  homonical. 

('HAP'I'KH  VI. 

l>IKFFJli:\TIAl.    IND!  .    1  1    >\. 

We  have  already  seen  that  tlie  h')ni.>i,i>;il  :i  mm-I  :hc  hoin-i  n.  ;il  .i, 
through  their  times  ;ire  hetera,  are  in  -|.:ii<'  homon.  i.  r,  ih,  \  ;iif  in 
the  same  where  at  any  given  point  of  lime  W-'  liavc  il-.  -en  ih -t  p,,. 
liomonicul  a  and  the  heterical  :,.  Ihongh  ,.  :  linic^  i,i  v  Im  :,. m  >ii, 
ure  hetera  in  space,  i.e,  one  a,  !»ai  a  certain  wh.  iv  and  llir  ."h.r  i.  his  an 
other  certain  where,  both  of  whirh  whercs  may  be  ...ciipi.-.l  ai  ihc  Mn.  linir. 
We  have  also  seen  that  hetera  lie  at  the  foundaii«.n  <>f  «■ -i -i!  i  .a,  and  that 
things  inter  se  similia,  and  also  things  inter  se  difVereniia.  am-i  be  inter  ><• 
hetera;  and  hence  either  similia  or  «lifrerentia  arc  the  e.-m-'-^  ol  .v.  ry  etbci. 
The  homonical  a,  and  the  helerical  a,  arc  i  it<  r  -e  h  tet.i,  ih.y  are  also  inui- 
se  similia,  hut  a,  and  b,  are  hetera  and  thev  aic  also  inter  se  (liMVrenti  i. 

Now  as,the  gregaria  of  aggregate  existences  aretne causes  of  .11  (  II,  •  k 
and  as  there  must  be  heterical  gregaria  concerned  in  the  production  of  ,v(  ly 
effect,  and  as  the  heterical  gregaria  concern<'d  nui»*t  be  inter  se  slmiiia  .»r 
difterentia,  it  is  the  province  of  ditlerential  induction  l..  eliminate  those  -re- 
garia,  which,  with  reference  to  the  causal  gregaria  of  an  etVect  existing  in 
either  of  the  aggregations  in  the  homonical  time  and  place  of  such  ert'ect.are 
differentia.  And  in  order  to  do  this,  we  must  first  make  helerical  and  homou- 
ical  inductions  of  aggregations,  (we  may  then  also  make  heteric^d  inductions 
of  gregaria,  which  is  as  far  as  Bacon  pushed  induction)  and  then  we  must 
make  differential  inductions  in  the  method  about  to  be  explained.  And  in 
order  to  understand  the  matter  thonuighly,  let  us  approach  the  subject  by 
first  clearing  the  way.  Suppose  we  take  two  aggregate  existences,  whose 
gregaria  we  know,  and  suppose  the  gregaria  of  the  first  aggregation  to  be,  a, 
b,  c,  d  and  e  and  no  more,  and  the  gregaria  of  the  second  aggregation  to  bj  a, 
b,  g,  h,  i,  and  no  more,  and  suppose  that  in  an  homonical  lime  and  place,  bv 
heterical  and| homonical  inductions  of  aggregations,  a  certain  eflict,  whicii 
we  will  call  a,  to  spring  from  thes^  helerical  aggregations:  then  we  can  not 


17 

tell,  whether  the  effect  a,  sprung  from  the  similia  a  and  a,  or  b  and  b,  or  from 
the  differentia  a  and  b,  b  and  b,  or  c  and  i  «S:c.  But  supp«)sing  the  efi'ect  to 
have  sprung  from  but  two  heterical  gregaria,  these  heterical  gregaria  must  be 
located,  one  in  each  aggregation,  and  not  both  in  the  same  aggregation,  oth- 
erwise the  effect  would  spring  up  in  a  single  aggregation  and  the  two  ag- 
gregations would  not  be  sine  quibus  non  in  the  homonical  time  and  [lace  of 
such  effect,  as  we  may  have  determined  to  be  the  case  by  a  previous  homonical 
induction,  and  without  a  previous  homonical  induction  of  aggregation  , 
differential  induction  of  causal  gregaria  can  not  proceed. 

Hut  suppose  we  take  five  aggregations,  whose  gregaria  we  know,  the 
the  gregaria  of  the  first  being  a,  b,  c,  u  aud  e,  and  no  more;  those  of  the 
second  a,  b,  c,  d,  and  f,  and  no  more;  those  o*"  the  third  a,  b,  c,  e  and  f,  and 
no  more;  (hose  of  the  fourth  a,  b,  d,  e  and  f,  and  no  more;  those  of  the  fifth 
a,  c,  d,  e  and  f,  and  no  more.  Now  we  can  conclude,  by  heterical  induction, 
that  the  effect,  which  springs  from  the  first  and  second  aggregations,  is  not 
caused  by  the  similia  e  and  e,  for  e  does  not  exist  in  the  second  aggregation; 
and  the  effect  which  springs  from  the  first  and  third,  is  not  caused  by  the 
similia  d  ant!  d;  aud  the  effect,  which  springs  from  the  first  and  fourth,  is 
not  caused  b}'  the  similia  c  and  c;  and  the  effect,  which  springs  from  the  first 
and  fifth,  is  not  caused  by  the  similia  b  and  b.  If  now  the  four  effects  be 
inter  :»e  similia  and  in  view  of  the  above  state  of  the  case,  we  look  upon  the 
second  aggregation,  we  conclude  by  heterical  induction  that,  in  that  aggre- 
gation e  was  not  a  sine  qua  non  of  the-eflect,  which  sprung  from  the  combi- 
nation of  the  first  and  second  aggregations;  and  hi^nce  a  simile  of  it  is  not  a 
sine  qua  non  in  any  (»ther  aggregation,  which  may  combine  with  a  simile  of 
the  first  aggregation  and  produce  a  siiuilical  effect.  And  in  the.othcr  instan- 
ces, we  may  eliminate  by  heterical  induciion,  d  from  the  third  aggregation,  c 
from  the  fourth,  and  b  from  the  fifth. 

We  have  not  been  speaking  above  of  any  other  effects  than  these  aris- 
ing from  the  given  combinations  of  the  given  aggregations,  whic.  by  pre- 
vious heterical  and  homonical  inductions  we  know  to  dc  the  aggregations 
containing  the  causal  gregaria,  and  the  gregaria  ef  each  of  which  aggrega- 
tions we  know  also.  There  may,  for  all  that  yet  appears,  however,  be  other 
aggregations  containing  causal  gregaria  of  effects,  which,  with  reference  to 
the  given  effects  spoken  of  above,  are  similia,  and  yet  the  causal  gregaria 
of  the  other  eff'ects,  with  reference  to  the  causal  gregaria  of  the  given 
effects,  may  be  differentia.  But  suppose  there  be  other  aggregations 
containing  other  causal  gregaria  of  an  heterical  effect  A,  these  other 
causal  gregaria,  with  reference  'to  the  causal  gregaria  of  the  homonical 
A,  the  effect  above  spoken  of,  must  be  either  similical  differentia,  in  which 
case  the  heterical  ett'ect  is  but  another  instance  of  like  causes,  i.  e.,  the  causal 
gregaria  of  the   homonical  A  being   the  Inunonical  diffe»entia,  a  in  the   first 


18 

aggregation   and  fin  the  second,  for  instance,  if  the  causal  gregaria  of  an 
heterical  A',Aand  A»  being  inter  se  similia,  be  similicalditferentia,  the  causal 
gregaria  of  the  heterical  A' are  the  similical  differentia  a'  and  T;  or  the  causK.'^ 
gregaria  ot  the  heterical  A,  with  reference  to  the  causal  gregaria  of  the  ho- 
monical  A,  must  be  differential  differentia,  i.  e.,  the  causal   gregaria  of  the 
homonical  A  C  being  the  homonical  differentia  a  and  t,  for  instance,  the  causal 
gregaria  of  a  heterical  a,  may  be  the  differential  differentia  e  and  g,  lor  instance 
for  aught  that  yet  appears.  But  in  no  case,  the  causal  gregaria  of  the  homonical 
A  being  the  homonical  differentia  a  and  f,can  the  causal  gregaria  of  an  heterical 
A  be,with  reference  to  the  causal  gregaria  of  the  homonical  A.similical  similia; 
for  the  similia  a  and  a,  b  and  b,  or  d  and  d,  &c.,  to  be  similical   similia  with 
the  homonical  differentia  a  and  b,  is  abgurd  and  impossible. 

But  supposing  the  causal  gregaria  of  an  homonical  A,  to  be  the  difftr- 
entia  a  and  f,  may  not  the  causal  gregaria  of  a  similical  A,  be  inter  se  similia, 
such  as  k  and  k,  y  and  y,  or  z  and  z  ?  Now  it  we  contemplate  the  causal 
gregaria  of  the  homonical  A,  and  those  of  the  similical  A,  im  the  two  a's  are 
inter  se  similia  in  every  respect,  and  as  each  oi  the  causal  gregaria  of  bollj 
a's  is  not  an  aggregation  but  a  simple  gregarium.  the  effect  produced  by  n 
and  f  inter  se  can  not  be  a  simile  of  an  effect  produced  by  a  and  a,  inter  se,  so 
long  as  homon  is  homon,  and  similia  are  similia;  and  if  a  can  origin;ite  upon 
a*  a  simile  of  the  effect,  which  f  originates  upon  a,  then  a  and  1  must  be  intir 
se  similia,  which  is  absurd.  If  a  certain  vibration  of  the  uimospliere  in  con 
nect.on  with  the  aparatus  of  the  ear  produce  a  certain  soun^.,  then  a  simile 
of  that  sound,  the  aparatus  of  the  ear  remaining  the  same,  can  not  be 
produced  but  by  a  simile  of  the  given  vibraUou. 

But  in  the  case  considered  above,  the  causal  gregaria  in  the  first  iii- 
ilance  being  by  supposition  the  differentia  a  and  f,  and  in  the  second  instance 
the  similia  a  and  a,  one  of  the  causal  gregaria  (a)  in  the  first  instance  ami 
one  (a)  in  the  second  are  inter  se  similia;  that  no  effects  inter  se  similia  can 
spring  from  such  sets  of  causal  gregaria,  is  evident.  But  an  effect,  an  ho- 
monical a,  having  sprung  from  the  causal  gregaria,  the  homonical  differentii 
a  and  f,  may  not  a  similical  A,  spring  from  the  similia,  gandg?  In  the  first 
instance  a  originated  upon  f,  an  homonical  effect  A,  and  we  see  that  g  cannot 
originate  upon  f,  a  simile  of  A,  unless  a  and  g  be  inter  se  similia;  but  in  the 
first  instance,  by  changing  the  mode  of  expression  without  affecting  in  any 
manner,  the  result,  f  originated  upon  a,  the  homonical  effect  A,  and  g  cannot 
originate  upon  a,  a  simile  of  A,  unless  g  and  f  be  inter  se  similia;  but  a  is  an 
liomonical  gregariura  and  g  is  an  homonical  gregarium,  and  inter  se  they  are 
differentia.  Now  two  gregaria  inter  se  differentia  can  not  in  their  action  be 
inter  se  similia  unltss  similia  and  difl'erentia  be  inter  se  similia,  which  is 
impossible.  And  if  a  cannot  act  towards  f,  as  g  acts  towards  g,  and  if  f  can- 
not act  towards  a,  as  g  acts  towards  g,  the  results  of  the  actions  betwcin  » 


19 

and  f,  and  between  g  and  g,  can  not  be  inter  se  similia.    And  an   homonicHl 
effect  a,  having  sprung    from  the  homonical  differentia  a  and  f,  we  may  rea- 
son in  like  manner  respecting  the  effect,  which  must  spring,  if  at  all,  from  the 
differential  differentia  g  and  h.    So  tuo  if  an  effect  spring  from  the  similia  a 
and  a,  no  similical  effect  can  spring  from  the  differentia  a  and  b,  c  and  d,  &c., 
nor  can  a  similical  effect  spring  from  differential  similia  as  b  and  b,  or  c  and 
C&c.    Ot  the  differential  elements  of   the   alphabet,   no  other  two  can  be 
conjoined  so  as  to  produce  the  sound  resulting  from   ab;  and   so  it  must  be 
throughout  nature.    And  hence  it  must  appear  that  effects  inter  se  similia  in 
every  respect  must  be  produced  by  similical  gregaria,  either  similical  simi- 
lia or  similical  differentia;  differential  similia  or  differential  differentia  can- 
not  produce  similical   effects.    And  therefore  if  two  or  more  aggregations 
come  into  the  homonical  time  and  place  of  an  effect,  we  first  find  by  heterical 
and  homonical  inductions  of  aggregations,  the  aggregations  from  which  the 
effect  sprung,  then  we  look  for  other  instances  containing  a  simile  of  one  of 
the  aggregations  from  which  a  similical  effect  sprung,  i.  e.,  we  vary  the  cir- 
cumstances, and  by  doing  so  we  are  often  able  by  heterical  induction  of  gre- 
garia to  eliminate  certain  gregaria  from  the  differential  aggregations  combined 
with  the  similia  of  the  other  aggregation  in  the  given  instance;  then  we  pro- 
ceed farther. 

And  it  must  be  remembered  that  two  gregarial  similii  cannot  exist  in 
tlie  same  aggregation.  Thus;  iron  possesses  hardness,  and  there  is  an  ho- 
monical hardness  in  this  piece  and  an  heterical  hardness  in  that  piece, 
and  inter  se  the  homonical  hardness  and  the  heterical  hardness  are  gregarial 
similia;  but  there  cannot  be  two  hardnesses  in  an  homonical  piece 
of  iron;  all  the  gregaria  in  a  single  piece  or  particle  of  iron  are  inter 
se  differentia.  Now  when  effects  are  produced  between  two  aggergations, 
these  aggregations  either  disappear  in  a  measure  and  merge  in  the 
effects,  as  in  chemical  compounds,  or  the  effects,  which  our  senses  witness 
are  grounded  in  one  of  the  aggregations  or  in  both.  When  oxygen  and  hy- 
drogen unite  and  form  water,  the  two  aggregations,  in  a  measure  merge  in 
the  effect— water,  i.  e.,  although  the  weight,  impenitrability,  &c.,  of  the  sepa- 
rate elements  remain  as  gregaria  of  the  compound,  yet  some  of  the  gregaria 
of  each  element  seem  to  have  disappeared  and  to  have  merged  in  an  effect, 
whese  gregaria  with  reference  to  the  gregaria  of  either  of  the  elements  are 
differentia;  but  if  we  apply  oxygen  to  steel,  we  witness  an  effect  grounded  in 
the  steel.  Having  now  cleared  the  way,  as  we  hope,  we  may  proceed  t«  diff- 
erential induction. 

Suppose  then,  that  we  take  a  certain  aggregation,  which  we  will  call 
A,  and  that  we  apply  the  aggregation  B  to  it,  and  we  find  a  certain  effect  x  to 
spring  up;  we  then  in  like  coniitions  apply  to  A,  or  to  a  simile  of  A,  the  ag- 
gregaliim  C,and  flndeitherno  effect  or  the  effect  y,  then  it  is  certain,  A  and  A 


20 

being  homon  or  inter  se  simil  lain  every  respect,  that  the  causal  grcs^ariura  of  x 
existing  in  b  has  no  simile  existing  in  C,  i.  e.,  that  each  of  the  gregaria  of  c 
and  the  causal  gregariuin  of  x  existing  in  B  are  inter  se  differentia. '  Suppose 
then,  that  we  can  discover  in  B  the  gregari.i  a,  b,  c  and  d,  for  instance,  and 
that  we  can  also  discover  the  gregaria  a,  b,  c  and  d,  in  C,  then  we  know  that 
neither  a  simile  of  a,  nor  of  b,  nor  of  c,  nor  of  d,  was  the  causal  gregarium, 
in  B  or  in  similia  of  B,  of  x,  which  sprung  from  the  horaonical  time  and 
place  of  A  and  B.  And  letting  the  capitals  A,  B,  C,  D,  &c.,  be  names  to  dis- 
tinguish aggregations  inter  se,  and  the  small  letters,  a,  b,  c,  d,  &c.,  be  names 
to  distinguish  eftects  inter  se,  we  may  make  the  following  tables  to  assist  the 
understanding. 


1st. 

A  and  B  produce  a 
A  and  C  produce  b 
A  and  D  produce  c 
A  and  E  produce  d 
A  and  F  produce  e 
A  and  G  produce  f  tfec. 


2d. 

B  and  A  prcnluce  a 
B  and  C  produce  g 
B  and  D  produce  h 
B  and  E  produce  i 
B  and  F  produce  j 
B  and  G  produce  k    »kc. 


Now  in  the  first  set  of  instances  in  the  homonical  time  and  wince  of 
the  effects,  if  we  desire  to  find  the  causal  gregaria  of  a,  which  exist  in  B, 
we  see  that  gregaria,  similical  with  the  causal  gregaria  in  B  of  the  effect  a' 
do  not  exist  in  C,  nor  D,  nor  E,  &c.,  and  hence  wherever  we  find  ag.euarium' 
in  C,  D,  E&c,  which  has  a  simile  in  B,  we  know  that  this  similical  Vcjra- 
rium  in  B  and  the  causal  gregarium.  or  each  of  the  causal  irrcgaria  ii^  B?  it- 
there  should  be  more  than  one  causal  gregarium  in  B,  are  inter  se  ditferen'iia. 
And  in  the  second  set  of  instances  we  may  deal  in  like  manner  with  the  gre- 
garia of  A.  And  after  that  we  have  differentiated,  by  differential  inductron 
as  in  the  manner  now  explained  above,  the  gregaria  in  B,  which  are  not  the 
causal  gregaria,  from  the  causal  gregaria,  we  may  dismiss  the  non  causal  gre- 
garia  from  our  consideration  and  look  further  into  the  matter. 

The  case,  however,  may  and  does  occur  in  chemistry,  where  two  a"-, 
gregations  will  not  produce  an  effect  without  a  third  aggregation  being 
brought  to  bear  upon  them,  and  then  differential  induction  is  rendered  still 
more  complicated  and  difficult.  Suppose  that  A,  B  and  C,  produce  the  effect 
a,  and  that  A  and  B  produce  b,  A  and  C  produce  c,  and  B  and  C  produce  d 
then  it  is  evident  that  the  causal  gregaria  of  a  existing  in  A  and  each  of  the 
gregaria  in  B  are  differentia;  for,  if  the  causal  giegaria  of  a  in  A,  have  simi- 
lia in  B,  then  B  and  C  would  produce  a  without  A.  And  in  like  manner  it 
is  evident  that  the  causal  gregaria  of  a  in  A  and  each  of  the  gregaria  in  C 
are  differentia,  and  the  causal  gregaria  of  a  in  B  and  each  of  the  gregaria 
in  A  are  differentia,  and  the  causal  gregaria  of  a  in  B  and  each  of  the  gre 


21 

garia  in  0  are  differentia.  And  hence  the  proximate  causal  gregaria 
of  a  must  be  in  b  and  C,  or  in  c  and  B,  or  in  d  and  A.  Now  if  A  and  B  really 
produce  no  effect  at  ail,  and  if  B  and  C  produce  no  effect  at  all,  it  is  evident 
that  tne  proximate  causal  gregaria  are  in  c  and  B.  And  if  c  be  a  permanent 
effect,  wa  may  then  deal  with  c  and  with  B  in  the  manner  abore  given;  but 
if  c  be  evanescent  we  are  not  able  to  manage  it  in  that  manner.  If  nitric 
acid  and  platinum  in  an  homonical  time  and  place  produce  no  effect,  and  if 
silver  and  platinum  in  like  conditions  produce  no  effect,  but  nitric  acid  dis- 
olve  silver,  i.  e.,  nitric  acid  and  silver  produce  an  effect,  which  we  will  call  c; 
and  if  nitric  acid,  silver  and  platinum  produce  an  effect,  which  we  will  call 

a,  then  it  is  evident  that  the  causal  gregaria  of  a  lie  in  c  and  platinum,  and 
we  must,  if  possible,  inquire  into  the  gregaria  of  c  and  also  into  those  of 
platinum  by  differential  induction  as  explained  above. 

But  suppose,  as  before,  that  A,  B  and  C  produce  the  effect  a,  and  that 
A  and  B  actually  produce  b,  and  A  and  C  produce  c,  and  B  and  C  produce  d, 
if  is  then  uncertain  whether  b  and  C,  c  and  B,  or  d  and  A  produce  a;  and  if 
the  eflects,  b,  c,  and  d  be  evanescent  and  not  of  a  permanent  character  per  se, 
so  that  we  cannot  examine  them,  we  can  make  no  inductions  respecting  the 
proximate  causal  gregaria  of  a.  If,  howtver,  b,  c  and  d  be  of  a  permanent 
character,  when  A  and  B  have  produced  b,  we  can  try  b  with  C,  and  >.o  of  c 
and  d;  and  in  tiiis  minner  we  can  differentiate  the  gregaria  of  c  and  d  fVom 
the  causal  gregaria  of  a. 

When  four  elements  enter  into  a  compound  in  a  binary  manner,  diff- 
erential induction  is  easy.     When  A  and   B  produce  a,  and  C  an<l  D  produce 

b,  and  if  a  and  b  Ivj  permanent  effects  and  they  produce  c,  we  may  first  make 
differential  inductions  of  the  causal  gregaria  of  a  in  A,  and  in  B,  of  b  in  C 
and  in  D,  and  then  of  the  causal  greir.iria  of  c  in  a  and  in  b.  But  it  u»ay  be 
that  A,  B,  C  and  D  contain  the  still  more  remote  causal  gregaria  of  a;  A  and 
B  may  produce  W,  A  and  (J  produce  c,  B  and  C  produce  f,  or  the  operation 
m:»y  be  still  more  complicated  and  then  tii('je  resultant  effects  produce  their 
effects  and  the  last  mentioned  effects  prwduce  still  others,  and  so  on  to  a 
given  effect  x  for  instance.  Organic  and  animal  life  is,  no  doubt,  produced 
in  this  manner.  But  however  complicated  the  matter  may  be,  the  principle 
of  differential  induction  in  any  case  has  a  simile  In  every  other  case,  and  it 
may  l)e  summed  up  in  the  following  differential  proposition;  whatever  gre- 
garia being  put  in  the  conditions,  in  which  certain  causal  gregaria  produce  a 
given  effect,  and  they  do  not  prodjice  a  simile  of  that  effect  and  the  causal 
gregaria  of  that  effect  are  difffc-rentia. 

CHAPTER  VII. 

SIMTLICAIi  INDUCTION, 

Having  treated  in  the  proceeding  chapter  of  differential  induction 
we  will  not  find  much  difficulty  in  understanding  similical  induction,  and  we 


need  not  spend  much  time  upon  the  subject.  But  in  •rder  to  assist  the  un- 
derstanding let  us  represent  aggregations  by  the  capitals  A,  B,  C,  &c.,  and 
their  effects  by  the  small  letters  a, b,  c &c.,  a>d let  us  form  two  tables  as  before: 

1st.  2d. 

A  and  B  produce  a  B  and  A  produce  a 

A  and  C  produce  a  B  and  G  produce  a 

A  and  D  produce  a,&c.  B  and  H  produce  a,  &c. 

Now  in  the  first  set  of  instances,  as  B,  C  and  D,  each  of  them  along 
with  A  produce  a,  A  remaining  the  same  or  a  similie  of  A  being  in  each 
instance,  the  respect,  in  which  B,  C  and  D  are  inter -se  similia,  is  the  causal 
gregarium  of  a,  existing  in  B,  in  C  aud  in  D,  &c.;  and  in  the  second  ?et  the 
respect  in  which  A,  G  and  H  are  inter  se  similia,  is  tlie  causal  gregarium  of 
a  existing  in  A.  And  if  A  and  B  produce  d,  and  then  d  and  C  produce  a, 
we  may  make  a  similical  induction  respecting  the  causal  gregaria  in  d  and 
in  C  in  the  manner  shown  above.  And  if  A  and  B  produce  d,  and  C  and  D 
prodace  g,  and  then  d  and  g  produce  a,  we  may  continue  our  inductions  in 
like  manner,  and  so  on. 

In  differential  induction  the  respect  in  which  aggresraiions,  one  of 
which  contains  causal  gregaria  of  a  given  effect  aud  the  others  not,  are  inter 
se  similia,  and  the  causal  grtgarium  in  the  one  causal  a^^i^reLraiiou  are  inter 
ie  differentia;  in  similical  induction,  the  respect  in  which  ajji^reirutions,  all 
uf  which  contain  causal  gregaria  of  a  given  effect,  are  inter  se  similia,  and 
the  causal  gregarium  of  the  given  effect  in  any  one  of  the  aggregaiions  c<.m 
pared  are  inter  se  similia.  And  if  two  aggre^r.-aions  containing  causal  gre- 
garia of  a  given  effect  and  compared  in  the  manner  abfive  stated  bo  inter  se 
similia  only  in  one  respect,  that  respect  is  the  causal  gregarium  of  flie  effect 
existing  in  each  of  the  aggregations.  The  principle  ot  similical  induction 
may  be  summed  up  in  the  following  similical  proposiiiou  ;  whatever  gregaria 
in  similical  conditions  produce  similical  effects,  are  inter  se  similia. 

CHAPTEH  VIII. 

INCOM.MEXSl'RAL    INDUCTION. 

We  have  seen  heretofore  that,  commensura  aud  incominensura  are 
relations  which  have  an  homonical  standard,  and  therefore  when  these  terms 
are  applied  to  aggregate  existences,  or  to  gregaria,  they  are  applicable  only  to 
those  existences,  which  are  inter  se  similia.  Thus:  a  mav  be  equal  to  n\  i.e., 
a=a*,  or  a<a',  a  aud  a'  being  inter  se  similia;  but  if  a  and  b  be  inter  se  diff' 
erentia,  a  cannot  be  equal  to  b,  i.  e.,  a=b,  and  a<  b,  are  propositions  witht.ut 
any  meaning,  just  as  much  as  when  we  say  that  this  sound  is  equal  to  that 
color.  Now  all  incommensural  effects  are  inter  se  incommensura,  by  reason 
of  the  incommensural  relations  of  time  or  of  space  or  of  both,  existing  be- 
tween the  aggregation  in  which  the  eftect  is  grounded  and  the  other  aggre- 
gation containing  causal  gregaria;  or  else  by  reason  of  the    incorameusural 


23 

relations  between  the  quantities  of  the  causal  gregaria  at  homonical  or  heteri- 
cal  times,  tb«  times  of  application  remaining  commensura,  and  the  spaces 
between  the  aggregations  remaining  commensura.  Thus;  an  hour  and  a  day 
are  incommensural  relations  of  time,  and  a  steady  rain  for  one  hour  and  a 
steady  rain  for  one  day  leaye  incommensural  effects  grounded  in  the  land 
from  the  incommensural  relations  of  their  times,  the  quantities  of  rain  falling 
in  commensural  times  being  commensura.  And  it  is  evident  that,  in  heteri  - 
cal  instants  of  time  the  causes  of  the  effects  grounded  in  the  laud,  the  rain 
which  falls,  are  not  homonical  but  similical;  yet  commensural  quantities 
falling  in  commensural  times,  the  effects  will  be  incommensura 
from  the  incommensural  relations  of  the  times  of  the  similical 
causal  gregaria  in  operation  to  produce  the  sums  t(»tal  of  the  effects.  Again; 
in  the  radiation  of  influences,  the  effects  of  those  influences  will  be  inter  se 
incommensura  from  incommensural  relations  of  space,  the  times,  and  quan- 
tities of  gregaria  in  aggregations,  in  which  the  effects  are  grounded,  being 
inter  se  commensura.     Thus: 


If  A  be  a  body  radiating  heat,  for  instance,  a  body  at  a  will  receive,  in 
commensural  limes,  more  of  the  radiated  influence  than  a  similar  and  com- 
inonsura!  body  at  u,  i.  e.,  the  ettect  grounded  in  the  body  at  a  and  the  effect 
irrounded  in  the  body  at  r,  will  l)e  incommensura.     Again: 


B 


0 


If  there  be  two  pit^c.-s  of  iron,  whoso  w;'ighls  are  inter  se  commensura, 
attached  to  the  lever  A  C,  the  onu  at  \i  and  the  other  at  C,  their  forces  exerted 
upon  a  body  at  A  will  be  inter  se  incommensura  fr*)ra  their  incommensural 
relations  of  space  from  the  fulcrum.  Aud  again  ;  if  in  commensural  relation 
of  time  and  space,  incommensura]  quantities  exert  their  influences,  the  effects 
will  be  incommensura. 

And  we  must  bear  in  min<l   that  the  iunommiusural  effects,  which  are 
to  be  the  subjects  of  inctimmensural   induction,  are  grounded,  and  witnessed 
by  our  senses,  in  one  of  the  aggregations  containing  causal  gregaria,  and  our 
object  IS  to  find  the  other  aggregii ion   or   aggregations   containing   the    re 
raaining  causal  gregaria.    Thus;  if  A  and  B  at  one  time  produce  a,  and  at  aa 


24 

other  time  A  and  6  produce  a*,  and  a  <  a',  these  incommensural  effects  are 
grounded  and  witnessed  by  our  senses,  either  in  A  or  in  B.  When  oxygen 
supports  the  combustion  of  coal,  the  effect,  which  our  senses  witness,  is 
grounded  in  the  coal.  Now  it  is  evident  that,  if  A  and  B  produce  no  effect 
whatever  upon  each  other,  they  cannot  produce  incommensural  effects:  If  A 
or  B  incommensurate  a,  A  or  B  must  be  an  ao^gregation  containing  causal 
gregaria.  And  hence,  letting  B  be  the  name  of  similical  aggregations,  if  we 
find  the  similical  effects,  named  a,  grounded  in  B,  and  these  effects  be  inter 
se  incommensura,  wc  may  then  look  for  some  other  aggregation,  A  for  in- 
stance, aid  make  observations  or  try  experiments  with  A  and  B,  and  by  in- 
commensural induction  determine  whether  or  not  A  contain  causal  gregaria 
of  a.  Thus;  commencing  with  incommensural  relations  of  space,  suppose 
the  effect  a  grounded  in  B  to  be  incommensurated  when  B  approaches  or 
receeds  from  A;  if  now  the  position  of  A  in  relation  to  other  aggregations 
be  changed,  i.  e.,  if  the  other  aggregations  among  which  A  is  situated,  be 
heteraled  by  changing  the  position  of  A  or  of  B,  and  a  be  iicommensuraled 
when  B  approaches  or  receeds  from  A,  then  it  is  evident  that  A  contain^ 
causal  gregaria  ot  a.  That  the  earth  contains  causal  giegaria  of  Uie  gravi- 
tation •f  terrestrial  bodies  towards  its  center  is  evident  by  inc<»iumcnsur:il 
induction.  On  the  oppoiite  sides  of  the  earth  at  the  sani'.'  time,  wh  ?n  Uh- 
same  stars  contain  between  them  and  the  earth  one  set  of  terrestrial  oodio 
and  the  earth  is  between  those  stars  and  an  other  set  of  terrestrial  bodies,  the 
gravities  or  effects  grounded  in  both  sets  of  bodies  become  incommensura  at 
incommensural  distances  from  the  earth's  surface. 

In  the  foregoing  example  we  have  seen  that,  fioni  the  incommensural 
relations  of  space  between  aggregations  containing  chusuI  gregaria  iiiciun- 
mensural  effects  arise.  Incommensural  quantilics  or  intensities  ot  cauual 
gregaria,  their  times  and  spaces  remaining  commensura,  produce  also  incom- 
mensural effects.  If  a  barometer  be  placed  under  the  receiver  of  an  air 
pump,  and  the  quantity  of  air  be  increased  and  again  diminished,  and  such 
incommensural  quantities  be  attended  with  incommensural  effects  upon  the 
baromettr  and  the  influence  of  all  other  objects  be  heterated  from  the 
homonical  time  and  place  of  the  effects,  it  is  evident  that  the  pressure  of  the 
atmosphere  is  the  cause  of  such  eflVcts.  And  hence  when  effects  giounded  in 
certain  aggregatioBS  are  incommensurated  and  we  can  perceive  by  obterva 
tion,  and  still  mort  when  we  can  we  can  make  the  experiment,  that  th«^  quan- 
tities or  intensities  of  gregaria  in  some  other  aggregation  are  corellatively 
incommensura,  and  we  can  also  heterate  other  objects,  we  may  be  assured 
that  the  correllative  incommensura  are  connected  with  the  effects  by 
causation. 

^  And  again:  the  relations  of  time  may  enable  us  to  make  incommen- 
sural induction  of   the  cauees  of  incommensural  effects.    Although  we  can 


25 

not  in  one  day  or  in  one  year  perceive  any  material  change  in  the  tails  of 
Niagara,  yet  other  objects  being  heterated,  and  the  water  continuing  to  flow 
over  from  year  to  year  and  very  gradual  changes  continuing  to  take  place 
ind  being  incommensura  in  incommensural  times,  other  things  being  equal, 
from  the  incommensural  relations  of  the  times  of  the  flowing  and  of  the 
wearing  away  of  the  rock,  we  can  infer  the  water  to  contain  causal  gregaria, 
in  the  absence  of  other  experience. 

The  principle  of  incommensural  induction  may  be  stated  in  the  fol- 
lowing Incommensural  propositions:  The  relations  of  the  times  of  causal 
gregaria  to  incommensural  effects,  spaces  and  quantities  being  commensura, 
are  incommensura;  the  relations  of  the  spaces  of  causal  gregaria  to  incona- 
mensural  effects,  times  and  quantities  being  commensura,  are  incommensura; 
and  the  relations  of  quantities  of  causal  gregaria  to  incommensural  effecto, 
limes  and  spaces  being  commensura,  are  incommensura. 

CHAPTEH  IX. 

COMMENSURAL    INDUCTION. 

We  have  seen  in  the  previous  chapter  that,  incommensural  effects,  timet 
being  commensura,  depend  upon  incommensural  relations  of  spaces  or  of  quan- 
tities between  the  causal  gregaria;    and,  on   the  other  hand,  eommensural 
effects,  whose  times  are  commensura,  depend  upon  eommensural  relations  of 
quantities  or  of  spaces  between  the  causal  gregaria.    And  we  must  always 
bear  in  mind  that,  not  an  homonical  gregarium  teut  heterical  gregaria  are 
the  causes  of  all  effects,  and  that  some  of  the  causal  gregaria  are  contained 
in  the  aggregation  in  which  our  senses  witness  the  effect  grounded,  and  somo 
ot  them  in  some  other  aggregation,  for  which  we  are  seeking  as  the  cause  of 
the  phenomenon,    when  a  magnet  attracts  iron-filings,  some  of   the   causal 
gregaria  are  in  the  magnet  and  others  in  the  filingsr'And  it  is  quite  evident  that, 
if  we  represent  the  quantity  of  the  causal  gregaria  existing  ip  a  certain  naagnel 
by  A,  and  the  quantity  existing  in  a  certain  piece  of  iron  by  b,  and  the  iron  of 
the  weight  c  be  attracted  through  a  certain  space  A  in  the  time  d,  a  magnet 
containing 2a  will  attract  iron  containing   2b  and  of    the  weight  2c  through 
the  space  A  in  the  time  d.    If  twelve  pounds  weight  attached  by  a  cord  will 
raise  twenty  pounds  upon  an  inclined  plane  through  the  space  A  in  the  tinae 
D,  twenty-four  pounds  in  like  manner  will  raise  forty  pounds.    And  as  in 
incommensural  so  in  eommensural  induction,  we  must  look  to  the  relations 
of  the  efl'ects,  which  we  witness,  and  then  to  the  relations  of  times  spaces  and 
quantities  of  other  aggregations  to  these  effects.    And  we  have  already  re- 
marked that,  neither  incommensural    nor  eommensural  induction  has  any 
reference  to  kinds  of  effects,  but  that  on  the  contrary  the  effects,  whether  they 
be  inter  se  commensura  or  incommensura,  are  always  inter  se  similia. 

Suppose  then  that  by  observation  or  experiment  we  find,  first  by  an 


mmmi 


Hi 


26 

liomonical  induction,  A  and  B  to  produce  a  in  the  space  b  in  the  time  c,  and 
in  other  parts  of  space  we  find  a  simile  of  a  grounded  in  a  simile  of  B;  we 
we  must  then  look  to  A  or  for  some  simile  of  A,  in  the  respect  of  the  causal 
gregtria  of  a  existing  in  A;  and  in  order  to  determine  which  object  is  this 
simile  of  A,  we  must  examine  the  quantity  of  causal  gregaria  in  A  and  in  B, 
and  their  relations  in|B,  and  also  the  quantity  of  gregaria  in  the  simile  of  B, 
in  which  we  witness  the  effect,  and  the  relations  of  this  simile  of  B  in  space 
with  other  objects.  And  if  we  find  an  object,  which  wc  may  call  y,  whose 
relation  to  the  simile  of  B  in  space  is  commensural  with  the  relation  of  A  to 
B,  times  and  the  effects,  a  and  a'  being  commensura,  so  far  y  is  indicated  as 
containing  causal  gregaria  of  a'.  And  if  now  by  a  change  of  spaces  we  can 
heterate  other  objects  from  relations  similical  with  the  relations  of  A  to  B, 
we  can  then  fairly  conclude  that  y,  contains  causal  gregaria  of  the  effect  a'. 
The  principle  of  commensural  induction  may  be  summed  up  in  the  following 
commensural  propositions:  The  relations  »f  space  between  thu  causal  gre- 
garia of  commensural  effects,  times  and  quantities  being  commensura,  are  inter 
se  commensura;  the  relations  of  quantities  of  the  causal  gregaria  of  com- 
mensural effects,  times  and  spaces  being  commeusuia,  are  inter  se  commen- 
sura; and  the  relations  of  times  of  the  causal  gregaria,  of  commensural 
effects,  quantities  and  spaces  being  commensura,  are  inter  se  commensura. 

CHAPTER  X. 

INDUCTION  PROMISCUOUSLY. 

From  what  has  been  said  in  the  previous  chapters  in  this  book,  it  must 
appear  that  in  making  inductions  we  use  for  the  most  part  two  cases  at  least, 
in  which  the  aggregations  are  not  homonical  hetera,  but  homonical  and 
heterical  hetera.  Thus:  if  we  wish  to  make  an  heterical  induction  of  the 
aggregations  A,  B  and  C,  which  in  one  instance  we  find  to  be  in  the  homoni- 
cal time  and  place  from  which  spring  the  effect  Z,  we  look  for  another  in- 
stance ot  the  effect  Z,  in  whose  time  and  place  A  nor  a  gimile  of  A  is  not  pres- 
ent: and  in  this  latter  instance,  we  do  not  find  the  homonical  B  and  C,  but 
we  find  similical  B  and  C.  And  hence  all  induction  proceeds  upon  the  truth, 
that  the  laws  of  nature  are  uniform,  or  that  similical  or  commensural  causes 
in  like  conditions  always  produce  similical  or  commensural  results:  and  this 
truth,  as  we  have  seen  heretofore,  is  establishea  in  our  minds  by  the  homoni- 
cal syllogism.  And  in  order  to  make  even  heterical  inductions,  we  must  have 
experience  gained  by  observation  or  experiment,  and  this  experience  depends 
upon  the  powers  of  the  mind  to  recognize  homon,  hetera,  similia,  differentia, 
commensura  and  incommensura.  We  find  by  experience,*  for  instance,  that  a 
certain  piece  ot  soap  will  not  cleanse  any  object,  with  which  it  docs  not  come  in 
contact;  and  if  now  we  call  this  certain  piece  A,  by  the  homonical  syllogism, 
a  simile  of  A  will  be  conditioned  in  a  similar  manner:  and  hence  if  we  find 


27 

an  instance  of  cleansing  in  whose  place  a  simile  of  A  was  not  present,  we 
make  the  heterical  induction  that  A  is  not  the  cause  of  cleansing  in  this  in- 
stance, and  not  a  sine  qua  non  of  such  effects.  Heterical  induction  of  aggrc- 
calions,  indeed,  goes  no  farther  than  the  particular  instance  frem  which  a 
certain  aggregation  has  been  heteraled.  If,  for  instance,  A,  B  and  C  are  the 
only  aggregations  present  when  the  effect  Z  comes  into  existence,  and  sup- 
posing A  to  have  been  a  aause  of  Z,  in  this  particular  instance,  we  know  by 
heterical  induction,  that  R  was  not  a  cause  of  the  homonical  Z,  but  for  all 
that  we  do  not  know  that  R,  if  in  the  place  of  A,  would  not  be  a  cause  of  a 
similical  Z.  For  the  causal  gregaria  existing  in  A  may  hav*  similical  gre- 
garia existing  in  R,  and  hence  R  would  also  be  a  cause  of  such  effects  as  Z- 
Heterical  induction  of  aggregations  does  no  i^.ore  than  remove  from  an  in- 
stance of  a  certain  effect,  certain  aggregations  as  sine  quibus  non,  and  thus 
clear  the  way  for  further  investigation. 

Homonical  induction  proves  directly  causation  mthe  instance  to  which 
it  is  applied;  but  the  homonical  induction  of  aggregations.althought  it  prove 
a  certain  aggregation  to  be  a  sine  qua  non  of  a  particular  effect,  yet  it  does 
not  prove  similical  aggregations  to  be  sine  quibus  nen  of  effects  similical 
with  that  particular  one.  Thus,  if  we  find  the  aggregations.  A,  B  and  C  in 
the  time  and  place  from  which  spring  the  effect  Z,  and  by  obserration  or  ex- 
periment we  find  B  and  C  without  A  in  a  similical  lime  and  place,  and  no 
effect  follows,  we  can  conclude  that  A  was  a  sine  qua  non  of  that  homonical 
Z,  but  we  can  not  conclude  that  similia  of  A  are  sine  quibus  non  ot  similia 
of  Z.  For  although  A  and  D  as  aggregations  may  be  differentia,  yet  the 
causal  gregaria  of  homonical  Z  existing  in  A  may  have  similical  gregaria 
in  D;  and  hence  D  also  will  contain  causal  gregariaof  similia  of  Z.  Arsenic, 
copper  and  lead,  as  aggregations,  are  inter  se  differentia,  yet  in  some  respects 
they  all  contain  similical  gregaria,  and  hence  each  of  them  is  a  poison.  And 
though  by  homonical  induction  of  aggregations  we  prove  a  cause  of  simili- 
cal effects,  yet  we  do  not  prove  the  only  cause.  But  if  we  can  make  an  ho- 
monical induction  of  gregaria,  we  will  prove  the  only  causes  of  similical 
effects.  Ic  is  very  seldom,  nowever,  that  we  are  able  to  obtain  the  data, either 
by  observation  or  experiment,  from  which  we  can  make  an  homonical  induc- 
tion ot  gregaria,  and  in  order  to  make  inductions  of  gregaria  we  are  obliged 
to  resr>rt  to  differential  and  similical  inductions. 

In  differential  induction,  which  presupposes  homonical  induction  of 
aggregations,  we  look  directly  at  the  gregaria  of  aggregations,  and  having 
applied  these  aggregations  severally  to  a  common  substance,  or  to  substances 
entirely  similia  inter  se,  we  note  the  gregaria,  which  are  inter  se  similia  in 
two  substances,  one  of  which  along  with  the  substance  A  for  instance,  will 
produce  the  effect  Z,  while  the  other  along  with  the  substance  A  will  not  pro- 
duce a  simile  of  Z,  and  then  we  differentiate  those  similia  from   the    causal 


28 

gregaria.  Sugar  and  soda,  for  instance,  will  both  dissolve  in  pure  water, 
these  capacial  gregaria  of  the  two  substances  are  inter  se  similia;  but  when 
vinegar  is  applied  to  soda  it  will  foam  and  boil,  while  when  applied  to  sugar 
it  will  not;  the  capacial  gregarium  of  being  held  in  solution,  therefore,  is  not 
in  soda  the  cause  of  the  ebulition  witnessed  when  it  is  put  into  acid.  In  the 
first  book  of  this  volume  we  spoke  of  facial  and  capacial  gregaria;  we  called 
the  color,  the  taste,  the  feeling,  the  smell  and  the  sound  of  objects,  their  facial 
gregaria,  because  they  present  such  appearances  to  our  senses.  In  realityi 
however,  all  these  things  are  capacial  gregaria;  and  the  only  difference  Is, 
that  facial  gregaria  are  perceptional  facts  immediately  noticed  by  the  mind, 
while  our  knowledge  of  what  we  have  called  capacial  gregaria  is  derived 
from  a  comparison  of  perceptional  facts.  Thus,  if  I  apply  sugar  to  my 
tongue  an  effect  is  produced  immediately  between  the  sugar  and  my  organs 
of  taste;  but  if  I  put  a  lump  of  sugar  in  water,  1  see  the  sugar  and  the  water 
and  I  may  see  the  sugar  dissolving;  I,  indeed,  make  an  induction  in  every 
Instance  to  arrive  at  the  knowledge  of  capacial  gregaria  of  aggregations. 
Now  in  making  differential  inductions,  we  always  arrive  at  the  knowledge  of 
similical  gregaria  in  various  substances  by  observing  the  facts  which  spring 
from  them  when  applied  to  similical  substances.  Thus,  supposing  our  or- 
gans of  taste  to  remain  in  similical  conditions  during  a  certain  time,  and 
during  this  time  we  taste  two  substances  and  find  their  tastes  to  be  exactly 
alike:  if  now  we  find  the  one  when  taken  into  the  stomach  will  net  as  an 
emetic  and  the  other  as  a  cathartic,  we  feel  assured  that  the  qualities,  the 
gregaria  which  are  similia  in  regard  to  our  taste,  and  the  gregaria,  which 
produce  in  the  stomach  differential  effects,  must  be  inter  se  difffjrentia.  And 
so  we  may  try  any  two  or  more  substances  with  pure  water  or  with  any  other 
thing,  and  in  this  manner  determine  similical  gregarial,  and  if  then  we  apply 
these  substances  to  some  other  thing  and  And  differential  effects,  we  may 
differentiate  the  similical  gregaria  from  the  causal  gregaria  of  a  given  effect. 
Differential  induction  does  not,  indeed,  determine  what  gregaria  are  causal 
gregaria,  but  it  merely  determines  what  gregaria  are  not  causal  gregaria. 
And  this  it  does  n©t  only  in  respect  to  a  particular  instance 
but  in  respect  to  all  instances  of  similical  effects.  In  the  compli- 
cated workings  of  nature,  however,  laws  are  frequently  antagonistic, 
and  when  one  prevails  over  another,  the  prevailing  one  must  always  be 
considered  the  cause  of  the  ensuing  change  which  takes  place,  while  the 
abrogated  law,  as  it  were,  is  not  the  cause  although  it  is  often  called  so.  And 
in  order  to  make  the  subjects  of  differential  and  similical  induction  clear,  it 
is  necessary  to  speak  of  this  matter  here.  If,  for  instance,  two  men  with 
rope  and  pullies  be  raising  a  rock  and  the  rope  break  and  the  rock  fall  to  the 
ground,  we  are  apt  to  say  that  the  breaking  of  the  rope  is  the  cause  of  the 
rock's  falling,  while  in  truth  the  causal  gregaria  of  the  rock's  falling  are  in 


29 

the  earth  and  rock,  and  the  rope  has 'nothing  to  do  with  it;  though  the  rope, 
before  it  broke,  was  a  cause  of  the  rocks  rising.    Every  change,  indeed,  is  an 
effect,  and  when  a  certain  positive  phenomenon  is  going  on  it  is  being  or  hag 
been  produced  by  certain  causes,  some  of  which  may  cease  to  act  and  then  the 
phenomenon  disappears,  in  which  case  we  are  accustomed  to  call  the  cessa- 
tion of  the  cause  of  its  production,  the  cause  of  its  disappearance.    We  are 
accustomed  to  say  that  the  want  of  wat«r  is  the  cause  of  the  death  of  a  fish 
up  on  the  land.    That,  however,  which  is  heterated,  the  absence  of  a  thing 
the  want  of  an  aggregation  or  gregarium,  can  not  be  the  cause  of  anything. 
Certain  laws  may  be  kept  in  operation  by  certain  gregaria  of  aggregation?^ 
and  then  certain  phenomena  exist;  take  away  one  of  the  aggregations,  the 
taking  away  of  which  is  truly  an  effect,  and  although  we  may  properly  call 
this  taking  away  of  the  aggregation  the  reason  of  the  cessation  of  the  phe- 
nomenon, yet  it  is  not  the  cause  of   such   cessation.    That  only  which   acts 
can  be  a  cause.    And  hence  although  there  may  be  and  is  plurality  of  causes 
of  similical  effects,  i.  e.,  the  causes  of  similical  effects  are  hetera,  yet  simili- 
cal effects  can  not  be  produced  by  differential  causes.    And  hence,  although 
many  aggregations,  which  as  aggregations  are  inter  se  differentia,  may  pro- 
duce similical  effects, yet  when  we  come  to  the  causal  gregaria  of  similical 
effects,  the   causal   gregaria  will    always  be  similical.    And   therefore,  the 
causal  gregaria  of  similical  effects  being  inter  se  similical,  we  at  once  know 
that,  of  two  aggregations,  one  of  which  produces  the  effect  and  the  other  not, 
the  gregaria  which  are  inter  se  similia  and  the  causal  gregaria  are  later  se 

differentia. 

In  similical  induction  we  compare  together  different  aggregations, 
each  of  which  we  find  to  contain  causal  gregaria  of  similical  effects  to  ascer- 
tain in  what  they  agree.  And  if  they  agree  but  in  one  respect,  this  respect 
we  know  must  be  a  causal  gregarium:  for  the  causes  of  similical  effects  are 
inter  se  similia  If  they  agree  in  several  respects,  we  can  not  tell  which  of 
the  similia  are  causal  gregaria,  and  we  should  try  by  differential  induction 
to  difierentiate  some  of  these  similia  from  the  causal  gregaria.  Thus:  if  A, 
B,  C  and  D  will,  each  of  them,  with  G  produce  similical  effects,  and  if  they 
all  agree  in  several  respects  so  that  we  can  not  tell  the  causal  gregarium  in 
either  of  them,  we  may  find  as  aggregregation  in  which  some  of  the  gregaria 
existing  as  similia  in  A.  B,  C  and  D,  exist  also,  and  yet  the  aggregation  along 
with  G  will  not  produce  the  effect.  That  crystaline  structure  is  not  the 
causal  gregarium  of  the  doublwrefraction  of  light  is  clearly  proven  by  differ- 
ential induction,  although  all  substances  which  have  hitherto  been  found  to 
cause  the  double  refraction  of  light,  have  been  crystaline ;  and  therefore,  if 
we  knew  that  they  did  not  agree  in  any  other  respect,  by  similical  induction, 
it  would  be  proven,  that  double  refraction  depended  upon  crystaline  structure 
alone.    Crystaliae  structure  may,  indeed,  be  one  of  the  cansal  gregaria  exist- 


30 

ing  in  all  substances,  which  refract  light  in  this  manner;  but  it  is  either  not 
a  cause  at  all.  or  at  best  it  is  not  of  itself  the  cause,  since  all  crystaline  sub- 
stanc«9  do  not  cause  double  refraction.  Differential  and  sirailical  inductions 
aid  each  other  in  the  search  after  causes,  and  neither  of  them  should  be  ne- 
glected  in  any  case,  if  they  can  be  applied. 

Incommensural  and  commensural  inductions  also  aid  each  other  in 
science.  That  the  oscilations  of  the  pendulum  are  cau&ed  by  th«  earth,  i.  e., 
that  the  earth  contains  causal  gregaria  of  these  oscilations,  and  also  that  the 
earth  contains  causal  gregaria  of  the  gravity  of  terestrial  objects,  was  proven 
by  incommensural  induction ;  and  then  Newton  by  commensural  induction 
proved  the  earth  to  contain  also  causal  gregaria  of  the  motion  of  th«  moon, 
and  established  what  is  called  the  universal  law  of  gravitation.  It  does  not 
seem  to  me  to  be  necessary  to  speak  farther  upon  the  six  methods  of  making 
inductions  which  we  have  endeavored  to  exhibit  in  the  previous  pages. 
These  six  methods  of  induction  with  the  aid  of  ratiocination  exhaust  the 
powers  of  the  human  mind  in  drawing  logical  conclusions.  And  whil« 
treating  of  our  subject  in  the  first  book,  we  saw  that  hetera  lie  at  the  founda- 
tions of  knowledge  and  that  homon  is  at  the  foundation  of  propositions;  and 
we  must  now  see  that  homon  is  at  the  foundation  of  all  induction  and  that 
ttie  homonical  syllogism,  sustains  the  truths  upon  whicli  every  induction 
proceeds. 

But  before  passing  on  to  further  considerations  it  seems  necessary  to 
make  a  few  remarks  upon  the  methods  of  induction  which  have  been  set  out 
by  J.  Stuart  Mill,  and  in  doing  so  we  will  not  go  into  a  lengthy  discussion, 
as  we  believe  that  the  student  who  has  mastered  the  preceding  pages  of  this 
book,  will  be  able  with  but  few  suggestions,  to  perceive,  what  we  consider, 
the  errors  of  Mr.  Mill.  Of  Mr.  Mill's  method  of  Residues,  we  shall  merely 
remark  that  when  we  have  subducted,  from  any  phenomena,  what  by  preri- 
ous  inductions  and  ratiocinations  we  already  know  to  be  due  to  known 
causes,  we  proceed  with  the  residue  by  some  one  or  other  of  the  six  methods, 
which  we  have  given,  and  that  there  is  nothing  peculiar  to  his  method  of 
residues,  so  that  it  should  be  considered  in  itself  a  particular  kind  ©f 
induction. 

In  what  Mr.  Mill  calls  the  method  of  agreement  there  is  the  mixing 
together  and  confounding  ot  what  we  have  called  heterical  induction  with 
similical  induction.  The  axiom  upon  which-Mr.  Mill  considers  this  method 
to  rest,  to-wit:  "Whatever  circumstances  can  be  excluded,  without  prejudice 
to  the  phenomenon,  or  can  be  absent  notwithstanding  its  presence,  is  not  con- 
nected with  it  in  the  way  of  causation,"  is  applicable  only  to  heterical  induc- 
tion, yet  Mr.  Mill  endeavors  to  apply  his  method  of  agreement  to  infer  caus- 
ation from  the  agreement  in  respect   to  the  presence  of  some  antecedent  in 


81 

every  case  from  which  the  effect  arises,  which  can  be  done  only  by  similical 
induction. 

Mr.  Mill's  method  of  Difference  corresponds  with  what  we  have  called 
homonical  inductions,  though  his  exposition  of  it  has  not  been  satisfactory 
to  our  mind.    What  Mr.  Mill   calls  the  Joint   Method   of   Agreement  and 
Difference,  we  regard  as  an  intermixture  of  homonical  induction  with  erro- 
neous views,  which  indeed,  have  reference  to  differential  induction,  although 
Mr.  Mill  had  no  conception  of   such  method.    It  is,  indeed,  quite  evident, 
that  if  A  will  produce  a  certain  effect  and  B  will  not,  the  causal  gregaria  ex- 
isting in  A  have  no  similia  existing  in  B,  and  if  now  we  could  examine  every 
substance   which  will   not  produce  the  given  effect  and   find   that  thej  all 
agree   in  not  containing  some  gregarium   which  is  contained   by  A,  there 
would  be  a  strong  probability,  and  nothing  more  than  a  probability,  that  this 
gregarium  was  a  cause  of  the  given  effect.    To  pursue  such  a  method,  how- 
ever, would  be  to  depart  from  true  induction  and  in  the  labyrinths  of  nature 
it  is  entirely  impractical,  and  of  very  little  value  could  it  be  done.    On  the 
other  hand  if  we  have  but  two  cases,  in  one  of  which  the  effect  springs  from 
A,  B  and  C,  while  in  the  other,  viz:  A  and   B,  the  effect  will  not  be  pro- 
duced, although  we  may  never  be  able  by  experiment  to  remove  and  again 
replace  C,  yet  the  two  cases  furnish  all  the  data  necessary  for  making  the 
homonical  induction  that  C  contains  causal  gregaria  of  the  effect.    We  con- 
clude that  there  is  nothing  in  Mr.  Mill's  Joint  Method  to  make  it  a  particu- 
lar kind  of  induction  and  further  that  a  great  part  of  hi«  doctrine  respect- 
ing it  is  erroneous. 

Of  Mr.  Mill's  method  of  concomttant  variations,  we  will  only  say  that 
he  does  not  make  any  reference  to  what  we  consider  to  be  the  true  principles 
involved  in  the  matter,  but  treats  of  cases,  some  of  which  are  to  be  deter- 
mined by  commensural  and  others  by  incommensural  induction. 

We  have  been  very  limited  in  our  remarks  upon  the  methods  of  Mr. 
Mill,  as  we  desire  in  this  book  to  take  the  afllrmative  and  not  the  negative 
side  of  questions.  Our  object  is  to  build  up  and  not  to  tear  down.  And  we 
propose  also  to  make  this  book  as  concise  as  possible  and  not  fill  and  enlarge 
it  with  criticisms.  We  may  dismiss  the  subject  of  the  inductive  methods 
here,  hoping  that  the  reader  will  be  able  to  understand  the  matter. 

CHAPTER  XI. 

HYrOTHESES. 

In  the  previous  pages,  we  have  dealt  only  wivh  those  principles  which 
are  brought  into  view  by  the  comparisons  of  truths  which  have  been  derived 
from  actual  facts  And  in  the  investigation  of  nature,  our  object  must  always 
be  to  find  out  what  actually  exists  and  how  it  operates,  and  not  to  assume 
certain  hypotheses  and  from  them  determine  how  nature  should  exist  and 


32 

operate.  He,  who  would  gain  any  scientific  knowledge  of  the  phenomena  of 
nature,  must  investigate  and  not  make  assumptions.  When  we  hav«  really 
gained  any  new  truth  in  nature,  we  do  not  rest  the  evidence  of  that  truth 
upon  an  hppothesis;  but  in  regard  to  all  certain  knowledge,  we  apply  the 
saying  of  Newton  "Hypotheses  non  fingo."  Yet  it  is  natural  for  man  to 
form  theories,  and  these  theories  often  direct  his  energies  towards  valuable 
results.  And  for  the  purpose  of  stimulating  the  mind  to  investigation  an 
hypothesis  may  be  laid  down,  aid  in  many  instances  for  that  purpose  an  hy- 
pothesis must  be  resorted  to.  No  man,  whose  object  is  to  search  after  truth, 
will  take  the  trouble  of  investigating  anything  unless  he  expects  to  find  out 
whether  something  which  he  has  in  view  be  true  or  not.  A  scientific 
hypothesis,  therefore,  is  a  subject  stated  for  debate,  in  which  arguments  pro 
and  con  can  be  brought  from  actual  facts  in  nature.  If  by  ratiocination  and 
induction  founded  upon  actual  phenomena,  the  hypothesis  can  be  proven, 
that  closes  the  debate  and  the  hypothesis  is  converted  into  a  truth,  the  evi- 
dence of  which  does  not  at  all  rest  upon  the  hopothesis.  And  hence  when 
we  have  laid  down  an  hypothesis,  our  object  must  be  to  prove  or  disprova  it 
from  actual  phenomena.  But  from  nature  we  can  prove  only  homon  or 
homa,  hetera,  similia,  differentia,  commensura  and  incomensura;  and  there- 
fore, scientific  hypotheses  may  be  divided  into  homonical,  hetera,  similical, 
differential,  commensural  and  Incommensural  hypotheses. 

In  heterical  hypotheses,  which  seem  to  be  the  most  convenient  to  be 
treated  of  first  in  order,  we  may  make  a  supposition  respecting  the  heterical 
existences  of  a  phenomenon;  or  granting  its  homonical  existence,  we  may 
lay  down  an  heterical  hypothesis  respecting  its  causal  grecjaria  as  sine  quibus 
non  of  certain  effects.  Thus:  as  a  simple  example  of  a  supposition  respect- 
ing the  heterical  existence  of  a  phenomenon ;  suppose  we  see  a  certain  horse 
in  an  enclosure  to-day,  and  to-morrow  we  see  a  horse  in  another  place  so 
much  like  the  former  that  we  are  uncertain  whether  it  be  the  same  horse 
which  we  first  saw,  we  may  make  the  heterical  hypothesis  that,  it  was  not  the 
same  ons,  i.  e.,  this  horse  and  the  one  we  first  saw  are  hetera,  and  then  we 
must  look  for  the  evidence  to  prove  the  hopothesis.  And  if  by  investigation 
we  find  that  the  first  horse  has  been  continuously  and  is  now  in  the  same  en- 
closure, we  have  proven  the  hypothesis  to  be  a  truth,  whose  evidence  does  not 
rest  upon  an  hypothesis,  but  upon  actual  relations  of  time  and  space.  And 
a  similar  example  might  be  given  to  illustrate  homonical  hypotheses  respect- 
ing the  homonical  existence  of  a  phenomenon :  we  need  not,  therefore,  speak 
of  this  again  under  the  head  of  homonical  hypotheses.  But  suppositions  re- 
specting the  causes  of  phenomena  are  also  useful  to  excite  endeavors,  and  we 
may  make  heterical  hypotheses  respecting  causation.  If  the  aggregations 
A,  B,  C  and  D  be  in  the  homonical  time  and  place  from  which  springs  the 
effect  R,  we  may  suppose,  for  instance,  that  D  is  not  a  sine  qua  non  of   the 


88 

R;  and  to  prove  our  hypothesis  we  find  another  instance  of  the  effect  R, 
from  which  D  was  absent  in  time  or  space.  And  again :  respecting  causal 
i^regaria,  if  the  aggregation  A  along  with  Z  will  produce  a  given  effect,  and 
Balso  along  with  Z  will  produce  a  similar  effect,  and  we  can  perceive  that  A 
possesses  gregaria,  which  B  does  not,  we  may  heterate  those  gregaria  con- 
tained by  A,  but  not  by  B,  from  the  causal  gregaria  of  ths  effect  produced  by 
A  and  Z,  and  thus  prove  the  heterical  hypothesis  respecting  those  gregaria, 
if  we  have  made  one.  And  we  have  already,  no  doubt,  gone  far  enough  to 
soe  that  heterical  hypotheses,  respecting  the  existence  of  any  phenomenon, 
to  be  worth  anything,  must  be  succeptable  of  proof  by  simple  heteration,  and 
that  heterical  hypotheses  respecting  causation  must  be  proven  by  heterical 
induction. 

Homonial  hypotheses  also  respecting  causation  must  be  proven  by 
homonical  induction;  and  until  they  are  so  proven,  they  are  not,  of  course, 
to  be  received  as  really  true,  however  useful  they  may  be  in  stimulating  in- 
quiry.    Homonical  inductions,  indeed,  are  best  and  more  frequently  made  by 
experiments  than  by  observations  upon  nature  in  her  undisturbed  processes 
offered  gratuitously  to  our  senses,  and  therefore  we  would  more  frequently 
resort  to  experiments  to  prove  any  homonical  hypothesis.    If,  for  instance,  we 
should  suppose  that,  it  is  the  equsil  pressure  of  the  atmosphere  upon  un- 
equally balanced  columns  of  water,  which  force  the  water  up  the  shorter  arm 
of  a  syphon,  we  could  make  experiments  from  which  an  homonical  induction 
of  the  real  cause  could  bo  brought  out  and  the  hypothesis  proven.    That  there 
is  an  ether  pervading  all  space  and  causing  light   by  its  vibrations,  however, 
can  not  be  proven  by  homonieal  induction,  aud  if  ever  proven,  (and  without 
being  proven  the  hypothesis  amounts  to  nothing)  it  must  be  proven  by  simil- 
ical induction.    An  homonical  induction  can  not  be  made  in  any  case,  unless 
the  existence  of  aggregations  containg  causal  gregaria  can  first  be   proven. 
If,  for  instance,  we  suppose  that   the  aggregations  A,  B  and  C,  produce   x, 
when  we  do  not  know,  whether  or  not,  A  really  has  an  existence,  we  can 
make  no  homonical  induction  in  the  case;  for  although  we  should  find  that 
B  and  C  alone  will  not  produce  x,  that  is  no  evidence  of  the  agency  or  exis- 
tence of  A  in  the  former  case     Homonical  hypotheses  respecting  causation, 
to  be  useful  in  increasing  our  stock  of  knowledge,  must  be  susceptible  of 
proof  by  homonical  induction.    And  no  hypotheses  respecting  the  existence 
of  an  aggregation  containing  causal  gregaria  can  be  thus  proven. 

We  may  also  make  differential  hypotheses  respecting  causal  gregaria, 
and  for  their  proof  we  must  resort  to  differential  induction.  We  might  sup- 
pose, for  instance,  that  the  quality  of  dissolving  upon  the  tongue  and  the 
causal  gregaria  of  the  taste  in  common  salt  are  diflerentia;  and  by  examin- 
ing other  substances  containing  this  quality,  we  could  prove  our  hypotheais. 
And  in  the  examination  of  nature,  as  differential  inductions,  though  they  do 


niSt  jJrovfe  w^at  the  tiausal  gregaria  are,  assist  very  much  itt  making  aimilical 
itfductions,  so  differential  hypotheses  should  be  assumed  and  tried  that  we 
may  have  every  help  in  unravelling  natures  complications. 

In  similical  hypotheses  we  assume  that,  the  causa!  gregaria  of  certain 
phenomena,  whose  causes  we  wish  to  ascertain,  and  the  gregaria  of  certain 
objects,  with  which  we  are  familiar,  are  similia:  and  if  their  effects  can  be 
sboWn  to  be  inter  se  similia,  we  prove  the  hypothesis.  Thus;  if  we  find  a 
particular  color  upon  white  paper,  we  may  assume  that  the  aggregation 
whatever  it  might  have  been,  containing  causal  gregaria  of  such  effect,  was 
similar,  in  respect  to  its  causal  gregaria,  to  some  object  with  which  we  are, 
familiar;  and  if  the  object  wtth  which  we  are  familiar  will  produce  upon  the 
same  kind  of  paper  the  same  kind  of  color,  we  prove  the  hypothsis.  If  all 
the  planets  contain  the  quality  of  attracting  iron,  they,  each  of  them,  possess 
gregaria  similar  to  the  lode  stone.  And  if  we  could  make  ourselves  certain 
of  the  existence  in  any  place,  of  an  ether,  whose  vibrations  would  produce 
light,  we  could  prove  the  ethereal  hypothesis. 

Respecting  incommensural  effects,  we  may  make  three  suppositions, 
viz:  first,  that  the  times  and  spaces  being  commensura,  the  increase  of  the 
qiiantity  of  gregaria  in  a  certain  obj«ct  incommensurates  the  effects;  second, 
that  times  and  quantities  being  commensura,  the  incommensural  efftcts  de- 
pend upon  incommensural    relations  of  space;  and  third,  that  spaces  and 
quantities  being  commensura,  the  incommensural  effects  depend  upon  incom- 
mensural relations  of  time.    And  having  made  our  hypothesis,  we  must  then 
find  the  proof  by  looking  into  circumstancei  varied  in  these  respects,  and  in 
which Ihe  effects  occurs.    But   in  making  our  hypotheses,  these  hypotheses 
must  have  i-eference  only  to  what  object  or  objects  contain  causal  gregaria  of 
the   incommensural  effects,  which   we  witness.    And  we  have  remarked 
several  times  already  that,  in  the  cases  from  which  an  incommensural  induc- 
•6on  can  be  made,  we  are  to  deal  only  with  similia,  commensura  and  inc«m- 
inensura  being  relations  inter  similia.    And  ihe  hypotheses  above  spoken 
'of  must  be  proven  by  incommensural  induction.    After  having  ascertained 
that  certain  objects  contain  causal  gregaria  of  given  effects,  we  may  make 
^!iyp"Dtheses  respectinsr  the  relative  increase  or  decrease  of   the  effects  to  the 
■  times,  spaces  or  quantities  of  causal  gregaria.    But  these  hypotheses  can  not 
'^e  verified  by  induction,  and  unless  they  can  be  verified   by  mathematical 
calculations,  they  are  merely  guesses.    We  are  frequently  obliged  to  make 
''mathematical  calculations  respecting  the  laws  of  variation  in  the  effects  de- 
peHcting  upoh  incommensural  spaces  and  times.    That  gravity  varies  inversly 
as  the  square  of  the  distance  is  not  an  induction,  but  a  truth  found  out  by  the 
application  of  mathematics  to  actual  phenomena.    Thai  the  spaces  passed 
oVer  in  successive  commensural  times  by  falling  bodies  are  in  the  relation  of 
''ih4  odd  ntrmbers  1,  8,  5,7,  &c.,  is  a  truth  of  the  same  kind,  i.  e.,  it  is  found 


35 

by  making  calculations  of  what  actually  oceurs,  as  observed,  in  this  respect, 
when  bodies  fall  without  being  impeded. 

Respecting  commensural  effects,  we  may  make  hypotheses  in  the  same 
manner  as  respecting  incommensural  effects,  and  we  must  seek  for  the  proof 
in  like  manner.  We  do  not  consider  it  necessary  to  make  further  remarks 
upon  hypotheses.  Every  hypothesis  respecting  causation  must  b«  proved  by 
induction ;  hypotheses  respecting  iheT^stioos  of  quantities,  times  and  spaces 
are  to  be  dealt  with  by  ratioci  nation. 

We  have  now  completed  our  view  of  ratiocination  and  induction,  so 
tar  as  we  propose  to  treat  of  them  in  comnK)n  language.  And  we  may  well 
consider  of  what  value  these  speculations  may  be  to  the  cause  of  science. 
And  merely  as  a  speculation  we  regard  the  previous  pages  as  not  ontirely 
unworthy  of  study ;  but  we  hope  yet  to  show,  that  practical  results  of  the 
grandest  kind  may  be  expected  to  follow  from  a  knowledge  of  the  principles 
therein  set  forth.  To  gather  up  an  exhibit  these  principles  in  formnlae,  and 
to  apply  them  to  the  actual  phenomenon  of  nature  will  be  our  object  ii^ 
Book  III.  -k 


T> 


/-: 


lib 
-  k 


BOOK  III. 

CHAPTER  I. 

SIGNS  IN  RATIOCINATION. 

In  the  two  previous  books  we  have  examined  the  foundations  of  rea- 
soning throughout  and  have  endeavored  to  explain,  by  the  use  of  common 
language,  what  we  have  considered  necessary  on  the  subjects  of  ratiocination 
and  induction.  Common  language,  however,  is  not  the  appropriate  vehicle 
of  recondite  ecience.  Without  the  assistance  of  symbols,  which  form  a  pe- 
culiar language,  Algebra,  which  consists  of  syllogisms  with  commensural 
and  incommensural  propositions,  could  not  have  been  brought  to  any  great 
perfection.  These  commensural  and  incommensural  propositions,  with  the 
syllogisms  constructed  upon  them,  however,  have  been  expressed  and  wrought 
into  Algebric  formula?,  which  can  be  transformed  in  various  ways,  and  there- 
by unexpected  and  grand  results  can  be  brought  to  our  apprehension.  And 
it  may  be  useful  to  inquire  whether  the  other  four  kinds  of  propositions  also 
can  not  be  expressed  in  symbols  and  reduced  to  formulne,  which  may  be 
formed  into  a  complete  system  of  abstract  and  exact  science.  That  such 
complete  system  of  science  may  and  will  be  constructed  in  the  future  by  the 
genius  of  man,  the  author  of  this  treatise  believes;  and  it  seems  to  him  to 
be  not  an  unworthy  undertaking  to  make  a  beginning  at  its  construction, 
"Which  may  be  an  incentive  to  call  to  the  work  others  of  more  favored  cir- 
cumstances and  greater  learning.  The  construction  of  such  system  will, 
therefore,  be  attempted  in  this  book.  And  we  will  commence  with  simple 
propositions.  ^ 

Let  the  sign  !r  stand  for  an  homonlcal comparison;  then,  ^a,  will  be 
equivalent  to  the  proposition  in  common  language,  a  and  a  are  homon.  Let 
the  sign  v  stand  for  an  heterical  comparison;  then  ava  will  be  equivalent  to 
the  proposition  in  common  language, a  and  a  are  hctera.  Let  the  sign  ||  stand 
for  a  similical  comparison;  then  a  ||  a,  will  be  equivalent  to  the  proposition 
in  common  language,  a  and  a  are  similia.  Let  the  sign  H-  stand  for  a  differ- 
ential comparison;  then  an-b  will  be  equivalent  to  a  and  bare  differentia- 
Let  the  sign  =  stand  (as  in  Algebra)  for  a  commensural  comparison;  then, 
a=a  will  mean  that  a  and  a  are  commensura.  Let  the  signs  >  and  <  stand 
(as  in  Algebra)  for  an  incommensural  comparison:  then,  a>a,  or  a<a,  will 
mean  that  a  and  a  are  incommensura. 


Now  by  the  use  of  the  foregoing  signs,  we  can  combine  the  six  kinds 
of  propositions  in  all  the  figures  and  modes  of  the  syllogism.  Thus  in 
mode  1st: 

aAa  or  aAa 
II    or         K-     • 
a' Aa'  or  a'  All 
.'.a  II  a',  or  .-.ahf-a'. 

And  tliese  syllosc'isms  will  be  true  irrespective  of  time  and  space,  i.e.,  if 
aA*  or  if  aVa,  or  if.  a  ||  a,  &c.  to-day,  they  always  have  been  and  always  will 
be  in  a  like  comparison,  so  far  as  time  and  space,  as  agents,  are  concerned. 

But  before  proceeding  further,  it  is  necessary  to  explain  the  manner  in 

which  simple   greiraria  of  aggregations  by   the  use  of  signs.    Let  the  first 

large  letters  of  Alphabet,  A,  B,  C,  «&c.,  stand  for   aggregations,  and  the  first 

small  letters,  a,  b,  c,  *fcc.,   for  gregaria,  then  a  syllogism  in  mode  1st  may  be 

thus  constructed : 

a  of  AAb  or,  a  of  AAb 
II    or,  H- 

a  of  BAb  or,  a  of  Bac 
.•.a  of  A  I!  a  of  B.  or,  .-.a  of  Ai+a  of  B. 

Now  if  a  stand  for  the  grcgarium — color,  we  may  interpet  the  syllo- 
gism thus: 

Color  of  AAb  or.  Color  of  AAb 
II   or,  H- 

Color  of  BAb  or,  Color  of  B  Ac 
.-.Color  ot  A  II  color  ot  B.  or,  .-.Color  of  A K- color  of  B 

And  these  signs  as  above  given  are  sufftcient  for  all  the  purposes  of  the 
singular  syllogism  and  of  the  singular  homonical  syllogism. 

But  for  the  purposes  of  the  Plural  syllogism,  we  wish  signs,  not  onlv 
to  express  the  comparison  between  the  terms  of  the  propositions  but  to  show 
also  the  comparisons  between  the  existences  exhibited  in  each  term.  And 
for  this  purpose,  we  need  but  combine  the  signs  already  given,  and  reading 
from  the  left  to  right,  interpret  the  sign  on  the  left  hand  as  an  adjective  and 
the  succeedmg  sign  as  a  noun.  The  following  table  will  show  the  use  of 
the  signs:  , 

Let  the  sign,  A  A,  indicate  homonical  homa. 


»( 

AV 

(( 

({ 

hfctera. 

i( 

All 

u 

C( 

•  similia. 

(( 

Ahf- 

t( 

ii 

differentia 

(I 

A~ 

(i 

»( 

commensura. 

(( 

A< 

u 

i( 

incommensura. 

(I 

VA 

(( 

he! 

erical 

homa. 

IC 

VV 

l( 

u 

hetera. 

i( 

V  II 

(( 

(( 

similia. 

(( 

VH- 

(4 

t( 

differentia. 

(I 

V  = 

(( 

u 

commensura. 

(( 

v< 

(( 

*t 

mcommensura. 

3 


l>i 


Let  the  sign,  ||  a  indicate  similical  homa 

((     ((       U  II  V  #         IL  ii  < 


{< 

({ 
t( 
(C 

k 

t> 

il 
{( 

CI 

(C 

i( 
(( 
(i 


11 

(4 

(I 
(( 


t( 


<t 


(( 


(( 


t( 


(( 


«( 


{(   u 


i( 


It 


C( 


(( 


t( 


(( 
<( 
i( 
« 

(( 
({ 
ct 

(i 
(( 
l( 
(( 
tl 
u 
(( 
(i 
(I 


u 


t( 


u 


II  V 

li  11 

II  H- 

11  = 

IK 
H-A 
H-V 
14-  II 
H-H- 
H-  = 
H-< 

=V^ 

=  11 

=  H- 

—  <: 

<  V 

<  A 

<  II 

<  H- 


tl 


11 

-11 

l( 
II 
(I 
II 
II 
II 
il 


ll 


II 


It 


li 
li 
It 
If 

ti 


hetcra. 
similia. 
difl'erentia. 
commeusura. 
incommeusura. 
differential  homa. 
"  hetera. 

"  similia. 

*•  differentia. 

"  commensuVa. 

"  incommensura. 

commensural  homa. 
*'  lietera. 

**  similia. 

••  differentia. 

**  commensura. 

**  incommensura. 

incommensural  homa. 
hetera. 
similia. 
differentia, 
commensura. 
incommensura. 

The  left  hand  sicn  indicates  tlie  comparison  between  the  terms  of  the 
propositions.  Thus;  in  the  equation,  a-fb=»-f-b,  the  sign  -  expresses 
the  comparison  between  a+b  and  u+b;  but  if  a=b,  then*  the  expression 
5*+^=  =aH-b  means,  not  only  that  we  have  m  equation,  but  also  that  the 
existences  exhibited  on  each  side  of  the  equation  are  inter  se  commensura 
1.  e.,  each  existence  on  one  side  of  the  equation  sign,  has  a  commensura 
tellow  on  the  same  side  and  on  the  other  side  of  the  signs. 

Now  with  the  loregoing  signs,  we  may  from  complete  syllogisms  in  all 
the  figures  and  modes.  And  commencing  with  the  first  four  kinds  of  pro- 
positions, let  two  dots  (  .•)  indicate  that  the  existences,  between  which  thev 
are  placed,  are  merely  grouped  together  by  comparison ;  and  let  AH,  without 
dots  between  them  mean  as  in  Algebra,  and  also  the  signs  -f  and  -  as  in  Al- 
gebra, and  the  following  paradigms  will  show  the  plural  syllngisui. 

PLURAL   SYLLOOrS.M— PARADIGM   IST. 


ll 


It 


it 


It 


li 
t« 
a 

t4 
M 


Mode  1st. 
A..B  A  A  A..B 


M 
li 


CDaaA  B 

.-.A.-Bjl  CD. 

Mode  5th. 
A..BA  AA'..B' 
A     A 
CDvA4'..B 
f.A..BvAC..D. 


Mode  2d. 
A..B  V  V  A'..B' 

A  A 
CDvvA.'B 
•.A..BVVCD 


Mode  3d. 

il.B  II  11  B  ..B' 

A    A 
C.D.  il  ||B..  B 
.B..B.  II  I!  CD. 


Mode  4th. 

A..B.if  jfCD. 

AA 
E..F.  hf  H-CD. 
'.indefinite. 


Mode  Olh. 

A..BAAA'  .B 

A  A 
CDii  aA'..B 
A.Bll  aCD. 


Mode  7th. 
A.BaAA.  ..B 

CDhhAA'..B' 
A.Bk-a^'.O. 


Mode  8ih. 
A..BVVA  ..B' 

A    A 

CD^VA'.B' 
•.A..BVVCD. 


4 

Mode  9th. 

A..Bv  vB  ..B 

AA 
CD  II  VA'..B' 
.-.indefinite. 

Mode  10th. 

A..BVVA'..B' 

vv 

CDff  VA'..B' 

.-.indefinite 

• 

Mode  nth.       1         Mode  12lh. 

.  A..BII  ||A'..B'      1  A..B1I  ||A'..B' 
A    A         j                     A      A 
:  CDa  !|A'..B'      1  CDv  ||A'..B' 
:.-.A..Bi|  llC.D.       i.-.indctinite. 

Mode  13th. 

A..BII  ||A'..B' 
A  A 

CDh-  II  a  ..b 

.-.A.Bhf  II  CD. 

Mode  14th. 
A..BH-H-CD 

A    A 
E.FAhfCD 

.•.A..BhhH-E..F. 

Mode  15th. 
A..BHHH-CD 
A    A 
E..FVH-CD 
.-.indefinite 

Mode  16th. 
A..Bh-1+CD 

AA 
E..FII  K-CD 
.••A..BH-H-E..F. 

The  first  paradigm  shows  the  plural  syllogism,  with  the  first  four 
kinds  of  propositions;  in  the  following  paradigm  the  first  two  and  last  two 
kinds  of  propositions  will  be  combined. 

PARADIGM  2d. 


Mode  1st. 

a..J[:aaa'..B' 

CDaaA'.7b' 
.•.A=..BaCD 


Mode  2d. 

A..BVVA'..B' 

A  A 
CDVV  A'..B' 
.•.A..BVVCD. 


Mode  3d. 

B..B=   rrB'..B' 

A    A 
CD=  =B'..B' 
.•.B..B=  =CD 


Mode  4lh. 

A..B<<CD 
A  A 
E..F«;CB 
.'.  indefinite. 


Mode  5th. 

A..BAA  A'..B' 

^  ^  .     A    A 
CDVaA'..B' 

•A-.B  V A  CD. 


I 


Mode  6th. 

A..BaA  A'..B' 

A    A 
CD=  A  A'.B 

.A..B=\C..D. 


Mode  7th. 

CD<aA'..B' 
.•.A..B<aCD. 


Mode  8th. 
A..B  VV  A'..B' 

CDaV  A'..B' 
.•.A..B  V  V  CD. 


Mode  9th. 
A..BVVA'..B' 

CD=viA 

.'.indefinite. 


Mode  10th. 

A.BVVA  ..B 

A     A 

.'.indefinite 


Mode  11th. 

A..B-:r:A'..B' 

A  A 
CD  A=A  ..B       , 
.•.A..B=  =CD.     I 


Mode  12th. 

.•.A..B=  -A'  .B' 

A     A 
CI)v=A  ..B' 
.-.indefinite. 


Mode  13th. 

A..B=«A  ..B' 

A    A 
('..D<— A'..B' 
.•.A..B<  —ii.D. 


Mode  14th. 

A..B<<CIX 
A  A 
E..FA<C..D 
1  .•.A..B<  <?  E..F. 


Mode  15th. 

A..B<  <  CD 
A   A 
E..Fv<CD 
.'.indifinite 


Mode  16th. 

A..B<<CD 
A  A 
E..F=<CD. 
.-.A..B<<E..F. 


Now  in  m-  de  1st,  of  paradigm  1st,  since  AaB,  the  first  premise  re- 
duces to  A\A;  and  as  CAD  and  AAB',  the  second  premise  reduces  to  C\ 
A' ;  and  hence  the  conclusion  will  be  A  ||  C.  And  in  mode  1st  of  paradigm 
2d,  for  similiar  reasons,  the  c<;nclusion  will  be  A=C.  It  must  also  be  ob- 
served that,  it  is  their  homonical  relations  inter  se  in  space,  which. makes  A 
A  B,  while  their  times  hcterate.     We  have  already  shown  heretofore,  that  the 


M: 


y 


O 


lioiiionical  A  to-day  anU  the  homonical  A  to-morrow  have  heterical  points  of 
li nu',  and  they  niayhave  Iietciical  wiikkks,  one  lo-dav  and  another  to-mor- 
roAv.  Eat  (or  the  present  we  vrill  suppose  that,  the  aggregalions,  with  wliich 
we  are  about  to  daal,  are  ill  and  continue  in  a  state  of  absolute  rest;  then, 
they  will  not  chuuge  their  wiiekes  in  space.  Now  with  the  use  of  the  sfgns 
already  adopted,  we  may  brins:  Uio  relations  of  lime  and  space  into  our  pro- 
positions and  exhibit  them  along  with  the  aggregations  or  gregaria.  Let  T 
stand,  not  for  time,  but  for  times  betweffu  which  there  may  be  a  comparison, 
and  let  S  stand  for  spaces  in  like  manner;  the,  the  prviposition  A  A  A',  in  or- 
der to  exhibit  the  relations  of  umcs  and  spaces  may  be  written  thus-  ' 

T.8. 

AAA': 

Which  proposition  may  be  put   into  common    language   as  follows:— 
The  hoMonical  A,  having  an  heterical  time  but  an  homonical  «pace  with  A 
IS  homonical  with  A'.    And  we  may  slate  the  first  prfemise  of  the  plural  syl- 
logism in  Alode  l..t  thus: 

W    AA 


A..BA  AA'..B'. 
And  this  proposition  may  be  stated  in  common  language  as  follows  — 
A  and  L,  whose  times  are  helera  and  i^uccs  homon,  havin-  heterical  lime^ 
but  homonical  spaces  with  A'  B  ,  who.e  times  are  hetera  but  spaces  homon 
are  homonical  with  A'  and  B  .  And  with  the  signs  and  letters  a6  they  are 
now  understood,  as  we  hr,p(.,  the  following  f.»ur  propositions  may  be  expressed : 

(^•^  (2)     ■  (3.)  (4.) 

^VAA  WAV  VVVA 


T. 


S. 


T. 


S. 


T. 


S. 


WW 
T.  8. 


A..BaaA'..B  .      A..BavA'..B'.       A..BVAA..B'.       A..BvvA'..B'. 

In  the  above  pn.posilions,  the  times  have  reference  to  the  temporal  re- 
ations  between  A..B..A..B'  and  the  mind  of  the  thinker,  i.  e.,  to  th«  rela- 
tions betwecii  the  objective  aggregations  aid  t<ie  subjective  conscious  truihi. 
Ami  we  can  easily  see  that  a  rose  bloomin.:;  on  the  tree  and  the  tree  itself 
liaveanhom(micaltime;butthe  rose  will  fade  and  pass  »\way,  while  the 
tree  may  yet  romaki,  and  hence  the  limes  of  the  rose's  existence  and  of  the 
tree  now  ar«  hetera.  And  the  limes  of  the  aggregations  exhibited  in  ihe 
abore  propositions  are  considered  in  their  velatiou..,  not  inter  «e,  but  to  un 
other  ex.slencc,  the   consciousness  of  the  ego.    But   if  we  consider   tho.e 


6 


aggregations  in  their  relations  of  time  inter  se  without  any  reference  to  any 
other  thing,  the  above  propositions  will  be  reduced  to  the  following: 


(I.) 

A    A 

T.   8. 


(11) 
A    V 

T.  8. 


(III.) 

A    V 
T     S. 


(IV.) 

AA    W 


T. 


8. 


A.  AVB.  AVA'.  A..BVVA'..B'. 

Now  if  we   reduce  the  premises  in  wodes  lit  in  like  manner  as  the 
propositions  last  above  ^iven,  we  will  have: 


T.8. 


(a.) 
2d.  premise 


■k.k. 


1st.,  premise 

A.  C. 

And  by  the  comparison  of  these  existences  viz.,  A  and  C,  we  must  draw 
the  conclusion  that: 


(b.) 

A    A    A    V  A   A 

T.  8.  T.  8.  T.  8. 


(c.) 

A  A  A  V  A   ^ 

T.  8.  T.  8.  T.  8. 


(d.) 

A   A  A  V  A  A 
T.  8.  T.  8.  T.  8. 


II       C. 


c. 


A       = 


C. 


(«.) 

A  A  A   V  A  A 

T.  S.  T.  8.  T.  8. 

A    <or  >    C. 


The  premises  in  mode  5th  reduce  as  follows: 


(f.) 


f.  8. 

• 

A. 

And  as 

T.8. 

A 

are  homon 

i.  e.. 

A  A    A  V   A  A 

T.  8.  T.  8 


'AX 


C        V      A. 

in  the  first  premise  and     __* '_   in  the  second  premise 

A, 
A   A     A   A     A   A 

Tl^  _^  ^'^       the  comparison  between  C 

A        A        A,         - 


(g.) 

A  A     ^  V  A  A 

and  A  makes  the  conclusion  ^^  ^^  _^ 

A         V  C. 


Tlic  premises  ill  iv.odes)  8  reduce  as  Inllows: 

A  V     A    ^     \'  V     A  V 
T.  !^.       T.         S.      T.S. 

A.B      V  V       A'..B\ 


1-ii.,  prtnuise, 


*iil,  ;>i(.n)i<c 


\    \ 
T.  S. 

A     B  , 


or 


A   V 
C.I) 


jij*  A.B  aiul  C.D  are 


homnnicnl  IicUmm,  luul  :is    T.I5. 


A  V      


(i.) 
\  A      \  \ 


A  A 

r.     s.    T.  s. 


A  ..n        A         V      A'..!;', 


thfiefi>"e  11k'  c.onclnsi'M],      ('.  8. 

A.B 


A  A 
T. 


\    V 


CD. 


Now  pronnsiiionR  ciiluT  (8)  nr  (III)  iiiidcilrHs  'hv  nonchisidns  in  modes 
1,  r>,  G  ami  7,  ;um»  proposilion  ciThiT  (4)  or  (IV)  und(Mli«'.s  llie  coiicliisionH  it) 
mouis,  2,  0,  4,  8,  9.  10,  11,  12,  13,  14,  15  and  16;  |V.r,  bimilia.  diireiontia,  com- 
luensiiiu  aul  iiicominoiisura  arc  alst^  iieiera.  (hiv  kno\vii'd;rt'  ot  lielera  and 
conricqucnily  <.t"  lioinon  dcpiTds  upon  tinif  and  .space;  but  our  kiio\vled;ie  »>f 
simiiia,  diircrciiha,  cninuunsiua  .wul  incomnicn  lu  a  does  not  depend  upon 
lime  and  space,  but  upon  t(»e  .i::«euHria  M'  agjnre:.;alir>ns.  And  these  substrala 
of  our  kno\vled«:^e  are  lo  be  ii.cpnred  int?)  (Vom  other  groiinils. 

rn.vn^K  ii 

Sli^NS  IN  IKDITCTION. 

In  heterical  induction  of  air»jreiratious,  we  find  two  or  mt)re  instances 
oi"  similical  effects,  and  we  u<%e  one  of  the  iniitanee^  to  eli^ninate  some  of  the 
airgregalions  fVoni  Uie  sTrie  qr.iUu8  non  in  another  instance.  Tlje  ugffrega- 
tions  of  the  two  or  more  ini.t'incei>*  may  be  synehrontjus  or.they  ma}'  not  b< . 
An  observation  mode  in  the  lime  (»f  Htuner,  if  correctly  made,  is  as  valuable 
for  one  of  tiie  instauces,  as  one  ma(ie  to-dav, although  the  a;rgregat ions  which 
caiue  under  observation  then,  may  have  ptssed  away  into  other  forms.  And 
in  making  experiments,  tiie  times  of  ilie  experiments  are  not  homon  but 
hetera.     But  the  aggregations  brougltt  together  in  any  one  instance  of  an  ob- 


servation or  experiment  have  homonical  times.  And  when  we  view  ametallc 
globe,  for  instance,  of  the  diameter  of  six  inches,  we  consider  it  as  occupy- 
ing an  homonical  WHERE,  thougii  the  wheres  of  its  particles  be  heter*. 
And  so  also,  if  we  bring  the  aggregiitions  A,  B,  C,  D,  &c.,  in  contact  with 
each  other,  we  may  tlien  consider,  the  result  as  an  aggregation  of  aggrega- 
tions and  as  occupying  an  honn)nioal  where.  Now  if  we  let  the  last  letters 
of  the  Alphabet,  v,  x,  y,  z,  stand  for  eft'ects,  and  let  the  sign  U  stand  for  cau 
satioii,  then  in  view  of  what  hns  been  said  above,  we  will  have  the  proposition. 


A   A 


(1.) 

V   V 
T.  S. 


A    A 


A..B..C..I).      V  V        A'..B*..C' 


2: 


V  V 
T.S. 


U 


X II X' 

And  as  x  and  x'  are  similical  effects,  they  can  be   produced  by  simili- 

« 

cal  hetera  and  in  order  lo  have  similical  hetera  EO  nomine  etin  numero,  we 
must  dismiss  D  in  the  first  term  Irom  the  sine  quibus  non  of  the  effect  x.  We 
may  then  find  another  instance  and  have  the  proposition: 


(!•; 

A    A 
T.  S. 

V  V 
T.    S. 

V  V 

'.^.  s. 

A"..B" 

A 

'..B'..C' 

11 

V    v 

T    S. 

U 





X" 

••••••    11    •••••« 

..X' 

And  this  proposition  enables  us  to  heterate  C.    Tiie   heterical  induc- 
tion of  irre-Niria  mav  be  represented  in  the  same  manner.  Take  the  proposition 

(2.) 


A    A 
T.  S. 

A   ..  B 

V  V 
T.*S. 

A   A 

V  V 
T.  S. 

f 

A   A 
•  T.  .->. 

C      ..    B' 

a..b..c..d  e..f..g  .h 

a..b..c.  e..f..g..h 

n 

U 

X 

•••••    11    •«• 

X' 

l|:l 


9 

Now  as  B II  B',  Ihejr  will  contain  a  like  number  of  similical  gregaria 
and  Jience  by  looking  at  C,  d  can  be  eliminated  from  the  causal  grega- 
lia  in  A. 

Homonical  induction  is  llie  reverse  of  heterical  induction.  Take  the 
proposition  respecting  aggregations: 


(3.) 


A   A 
T.  S. 

V  V 
T.  8. 

A   A 
T.  8. 

A..B..C 

» 

V  V 

V  V 
T.  S. 

K- 

B'..C' 

X 

n 

0.  or 

Now  H8  we  desire  to  have  similical  effects,  i.  e.,  x  and  x',  they  must  bo 
prmluced  by  similical  lietera,  eo  nomine  et  in  numero,  and  by  looking  at  the 
terms,  we  see  that  A  must  be  added  to  the  second  term,  i.  e.,  that  A  was  a  sine 
qua  non  of  the  effect  x. 

In  differential  induction  we  first  clear  the  way  as  much  d*  possible  by 
heterical  induction  of  gregaria  and  then  take  the  proposition: 


A    A 
T.  S. 

A.      .B 


a..b..c..d  i.k.&c. 


n 


(4.) 

V  V 
T.  S. 

V  V 


V  V 
T.  8. 


A    A 
T.  S. 

C.     .B 


H..b..e..f  i..k..&c 


n 


X H- 0,  or  y. 

And  now  as  B  !|  B',  their  gregaria  are  similical  differentia;  aad  if  A  || 
C,  we  should  have  had  similical  eff-cts;  but  as  the  effects  are  differentia,  their 
causal  gregaria  in  A  and  in  C  are  differentia:  and  hence  the  similical  grega- 
ria in  A  and  C  may  be  differentiated  from  the  causal  gregaria,  i.  e.,  a  and  b 
and  the  causal  gregaria  of  x  in  A  are  differentia. 

Similical  induction  is  the  reverse  of  differential   induction;  lake  the 
proposition. 


10 


A    A 
T.  S. 

A.      .B 


a..b..c..d  i..k..&c. 


U 


(5.) 

V   V 
T.  S. 


V    V 


V    V 
T.  S. 


A   A 
T.  8. 

C.      .B' 


a..b..c..f  i..k..&c. 


21 


X II X' 

Now  as  X  II  x',  tliey  have  been  produced  by  similical  gregaria,  and  as 
B  11  B',  we  must  find  similical  gregaria  in  A  aufl  C,  and  we  find  a  and  b  in 
both;  therefore  the.se  gregaria,  or  one  of  them  at  least  is  a  causal  gregarium. 

We  must  notice,  that  in  »ur  propositions  for  making  heterical  and 
honiouical  induetiens,  wv  rej*resent  the  aggregations  by  the  signs  between 
the  terms,  merely  as  lietera.  This  mutt  necessarily  be  the  case;  for,  v»'e  are 
eliminating  and  aggregating  hetera  by  those  processes.  In  differential  and 
similical  inductions  also  we  must  represent  the  aggregations  by  the  signs, 
raerelv  as  hetera.     For,  if  A..B 


It 


and  A  i|  B,  we  know  by  ratiocination  that  eimilical  similia  will  produce  simi- 
lical effects;  and  if  Ai+6,  we  know  that  similical  differentia  will  produce 
similical  effects.  But  in  the  al>ove  inductive  propositions,  B  i|  B'  and  Ah-C, 
as  aggregations,  and  we  desire»o  find  in  A  and  C,  the  respects,  the  gregaria 
inter  se  similia  and  to  make  an  inference  respecting  them  and  this  can  be 
done  only  by  using  the  heterical  signs  between  the  terms. 

In  incommeusurl  induction,  there  are  three  cases;  1st,  times  and  spaces 
being  commensura,  the  quantities  are  incommensura;  2d  the  times  and  quan- 
tities lieing  commensura,  the  spaces  iU'e  incommensura;  3«1  the  spaces  and 
quantities  being  commensura,  the  times  are  incommensura.  Let  us  suppose 
that  we  witness  the  effect  in  B  and  B',  tken: 


A  V 
T.  8. 

A..B 

X... 


A  V 
T.  8. 


,y 


V  V 
T.  8. 


U 

..X' 


-.>j 


11 


13 


A  V 
T.8. 

(7.) 
=  V  <v 

T.       8. 

A  V 
T.8. 

A..B 

=            V 

V  V 

T.  S. 

> 

A'..B' 

X. ..  t..  .  . 

X' 

^.l 

(8.) 

<  V  =  V 

T.             8. 

il 

A.B 

V 

V  V 
T.  S. 

<  

A.B' 

X ^. 

•2^ 
X' 

Commensural  induction  brings  a  simile  of  one  of  the    aggregations, 

irhich  we  hare  determined  by  incommensural  induction  to  contain  causal 
gregaria  of  a  given  effect,  an4  some  other  aggregation,  about  which  we  are 
uncertain,  into  relations  commensural  with  the  relations  between  the  aggre- 
gations, which  we  know  to  coatain  causal  gregaria  <>f  such  effects.  And 
these  relations  are  threefold,  hence : 


^.  s. 

(9.) 

ic  V  =^  V 

T.            S. 

• 

^'.H. 

A.B 
21 
X 

=             V 

• 

V    V 
T.8. 

C.B' 

X' 

M 


Which  proposition  brings  C  and  B'  into  commensural  rclalions  with 
tlie  relations  of  A  and  B,  and  when  that  is  done  we'find  the  commensural 
effect,  and  hence,  as  B  ||  B',  we  cenclude  that  C  contains  similical  gregaria 
with  A.  If  we  should  take  the  second  term  of  psoposition  (8,)  as  the  first 
term  of  an  inductive  commensural  proposition  wc  will  have: 


u 

(9.) 
=  V  =  V 

T.         ^. 

fs'. 

A'..B' 

=        V 

'          VV 
T.8. 

C.B' 

U 

r 

X' 

U 

X" 

If  we  cannot  thus  bring'the  aggregations,  which  we  are  investigating, 
into  commensural  relations  as  above,  and  find  commensural  effects,  wc  may 
yet  frequently,  by  mathematical  calculations,  find  what  would  be  the  effect,  if 
such  commensural  relations  were  realized;  and  this  will  answer  the  purpose. 

CHAPTEK  III. 

HKTERICAL  IVDUCTION  APPLIED. 

In  the  two  previous  chapters,  we  have  given  formulae,  which,  when 
carefully  considered  and  fixed  in  the  mind,  will  assist  the  understanding  in 
investigating  nature.  Observations  and  eitperiments  must  furnish  the  data 
but  the  inferences  to  be  drawn  from  those  data  must  be  dictated  by  a  sound 
philosophy.  And  the  formulae,  which  we  have  ^iven,  will  not  only  aid  the 
mind  in  making  proper  inferences,  but  also  in  lookiag  for  the  kind  of  instan- 
ces,  from  which  alone  legitimate  inferences  can  be  drawn.  And  in  applying 
the  foregoing  principles,  it  will  not  be  necessary  for  us  to  bring  the  cases 
noticed  into  the  exact  form  of  the  formulae,  as  the  reader,  who  has  mastered 
ihesulyect,  can  easily  do  that  for  himself  We  wish  merely  to  show  the 
utility  and  impsrtauce  of  the  subject,  by  illustrations  from  cases  in  which 
these  principles  have  led  to  scientific  discoveries,  though  the  investigators, 
perhaps,  were  entirely  ignorant  of  the  processes  heretofore  explained.  And 
it  will  not  be  necessary  to  furnish  many  illustrations  to  show  what  may  be 
expected  to  follow  trora  a  thorough  knowledge  of  these  processes  by  the 
scientific  men  of  the  world,  who  are  engaged  in  the  several  departments  of 
science.  Our  illustrations  may  be  taken  from  any  department  of  Knowlcdgt 
for  our  principles  apply  to  every  branch    of  science.     We   will   commence 

with  heterical  induction. 

Among  all  the  varieties  of  material  forms,  which  surround  us  in  the 
world,  chemists  have  been  able  to  find  fifty-five  elementary  substances,  i. 
t.  Substances  whwe  particles  are  inter  se  similia.  And  from  some  or  other 
of  these  elements,  mineral  compounds,  vegetable  organisms  and  animal  or- 
ganizations are  produced.  Now  nature^s  bbratory  can  be  entered,  in  the 
first  instance,  only  by  indjjction ;  we  cannot  commence  with  the  simple  ele- 
ments and  reason  a  priori,  or  a  posteriori,  without  first  having  made  indue- 


if 


13 

tions.  There  is  no  evideaoe,  about  which  we  at  present  know  Anything,  to 
establish  any  belief,  that  what  now  are  called  elements,  are  really  compounds; 
and  when  we  find  the  number  and  kinds  •f  elements,  which,  from  any  eom- 
pound,  or  oro:anization,  we  conclude,  that  we  have  all  the  sine  quibus  non 
and  because  none  other  are  present,  i.  e.,  ky  heterical  induction.  But  be- 
cause a  certain  number  and  kin*is  of  •Itments^are  found  in  certain  instances, 
or  even  in  all  instances  known  tons,  v?c  are  n«t  certain  that  each  one  of 
them  is  a  sine  qua  non  of  th«  -iven  effect ;  althouijh  this  false  kind  or  reason- 
ing per  enumerationem  simplioem  is  still  employed  by  writers  upon  the 
physical  scieiccs. 

In  the  organiEations  of  animals  we  lind  an  animus  or  life  principle 
vis  vitffi,  and  this  princii^le  has  been  said  to  possest  and  exert  a  force  sui 
generis  upon  the  elements  and  to  impart  to  them,  wh«u  taken  into  the  stom- 
ach, an  unusual  action.  And  although  this  life  principle  exists  in  all  ani- 
mals, yet  the  theory  respecting  it?  force  on  the  elemeats  (and  it  is  nothincr 
bMt  a  theory)  has  recently  been  disproved  in  a  measure  at  least  in  the  mos^t 
satisfactory  manner  by  heterical  induction.  It  has  been  shcxwn  that  hard 
boiled  albumen  and  muscular  fibre  can  be  dissolved  by  adding  a  few  drops 
of  muriatic  acid  to  a  decoction  of  tli«  stomach  of  a  dead  calf,  precisely  as  in 
the  stomach  of  a  living  animal.  This  one  instance  heterales  the  vim  vita- 
from  the  sine  quibus  non,  and  leaves  the  stomach  t  act  upon  chemical  prin- 
ciples in  dissolving  the  food;  and  if  the  known  principles  of  chemical  trans- 
formation do  not  yet  sufficiently  account  for  digestion,  it  must  be  further  in- 
quired iito.  Physiologists  have  also  attributed  the  foimation  of  formic  acid 
oxalic  acid,  urea  &c.,  in  the  body  to  the  force  of  the  ris  vit^e-  yei  each  of 
these  can  be  formed  in  the  lakratory  of  the  chemist,  and  con^quently  it  is 
proved  that  vis  vit«e  i-  not  a  sine  qua  non.  True  heterical  induction  thus 
dispells  mystic  tkeories  and  opens  the  true  road  lor  inquiry. 

Chemists  have  contended  that  vegetable  !5bre  in  a  state  of  decay  which 
IS  called  humus,  is  absorbed  by  plants  ai.d  is  necessary  to  Ui^ir growth-  yet 
this  humns  can  be  separated  by  heterical  induction.  For,  although  'this 
humus  IS  present  im  most  soils,  yet  "plants  thrive,"  as  we  are  informed  by  Dr 
Leibig  "in  powdered  charcoal,  and  may  be  brought  to  blossom  and  bear 
fruit  If  exposed  to  the  influence  of  the  rain  and  atmosphere;  the  charcoal 
may  be  previously  heated  to  redness.  Charcoal  is  the  most  'indlflerent'  and 
most  unchangeable  subsUace  known;  it  may  be  kept  for  centuries  without 
Change,  and  is,  therefore,  not  subject  to  decomposition."  Now  one  suck  case 
•fljust  cited  from  Dr.  Leibig,  who  rea^ns  more  philosophically  than  mo.i 
chemists,  completely  hetorates  the  absorption  of  humus  from  the  sine  qoibus 
noD.  Leibig  contends  further,  that  humus  merely  furnishes  carbonic  acid 
for  the  atmosphere  surrounding  the  roots  and  stafk  of  the  plant,  and  that  thii 


U 

carbolic  acid  is  a  sine  qua  non.    This,  howewr,  cannot  be  proved  by  heteri- 
cal induction,  which  is  the  oqly  subject  that  concerns  us  at  present. 

We  find  that  several  kinds  of  opium  contain  maconic  acid,  and  from 
the  examination  of  such  kinds  alone  wilh(iUl  a  true  philosophy  by  which  to 
test  nature,  we  w(mlderroMwously  conclude  maconic  acid  t(.  be  asiuc  qua  non 
of  opium  as  an  anadyne  and  soporifl'r,  but  there  are  other  specimens  of  opium, 
which  do  not  contain  a  trac(!  of  tiiis  acid,  and  yet  thry  produce  similical 
cttectr*.  By  heterical  induction  also,  wr  establish  the  truth,  that  volition  and 
the  mind's  command  of  the  nervous  apparatus  are  not  sine  quibus  non  of 
nutrition  in  animals.  For,  in  those  parts  of  the  body,  which  have  been  para- 
lyzed and  which,  llierefore,  are  destitute  of  feeling  and  not  subject  to  the 
mindB  control,  nutrition  still  proceeds  without  inlerrupiion.  Oxygen  may 
be  condensed  into  a  liquid  by  pres>iure,  in  which  state  it  posses  those  grega- 
ria,  which  distinguish  a  liquid  from  a  gass;  Hiid  yet  in  either  state  its  actions 
upon  other  substantts  are  inter  se  «iuiilia;  and  those  distinguishing  gregaria 
some  in  the  nne  and  suiiie  in  the  Mther  state,  can  be  heterated  Irom  the  causal 
gregaria  of  the  effects  of  oxygen.     Wen«*ed  not  illustrate  further. 

CHAHTEU  IV. 

HOMONFCAL  INDUCTION    APPLIED. 

We  have  henM<»fore  obst*rved  that  heterical  induction  does  not  deter- 
mine causes,  but  merely  clears  the  way  si*  tliat  homouical  i*  duction  can  be 
made  more  easily  applicable  io  any  given  case.  Now  we  find  that  animals 
having  lungs  respire  the  atmosphere,  and  so  long  as  respiration  continues, 
the  circulation  i)f  the  blood  and  life  and  heat  exist,  but  let  respiration  be 
prevented  and  denlh  ensues;  by  honionical  induction,  lhercf»re,  the  atmos- 
phere IS  one  of  the  causes  of  life  and  heal  in  ^uch  animals.  And  upon  ex- 
amination of  the  atmosphere,  we  find  it  to  contain  frequently  carbonic  acid, 
water,  some  earthy  matters  and  oxygen  and  nitr(>geu.  The  earthy  matters, 
carbonic  acid  and  water  can  be  removed  from  the  causes  of  the  etfecls  of 
respiration  by  heterical  induction;  but  if  we  remove  the  oxygen,  these  effects 
immrdialcly  cease,  and  hence  it  is  certain  that  oxygen  is  a  sine  qua  dou. 
And  by  heterical  induction  we  can  remove  all  elements  from  the  sine  quibus 
lum  ot  the  growth  of  mamihalia  excepting  those  contained  in  milk;  for  the 
health  and  grt)wth  ot  the  young  may  be  promoted  by  milk  alone.  N«w  we 
find  milk  to  contain  caseine,  a  compound  containing  a  large  proportion  of 
nitrogen;  sugar  of  milk,  in  which  there  are  large  quantities  of  oxygen  and 
hydrogen;  lactase  of  soda,  phosphate  of  lime,  common  salt  and  butyric  acid. 
Is  each  of  these  elciuents  a  sine  qua  non  ?  A  horse  may  be  kept  alive  Qpon 
potatoes,  in  which  the  quantity  of  nitrogen  is  small,  but  he  does  not  thrire, 
and  if  deprived  of  all  food  containing  nitrogen,  he  dies.  Mammalia  cannot 
Htc  withonlH  salt,  nor  can  any  one  of  the  consiiluenis  of  milk  be  wanting 


15 

for  any  threat  length  of  time  without  a  marked  influence  upon  tiie  healtli  of 
the  animal.  Experiments  showing  such  truths  furnish  the  data  for  homoni- 
cal  inductions.  Plants  cannot  grow  if  either  hydrogen  or  carbonic  acid  be 
wanting,  and  hence,  these  art*  sine  qui  bus  nun. 

And  aixain,  we  see  that  if  tiie  blood  be  taken  from  animals,  the  imme 
diately  die;  that  blood  is  a  sine  qua  non,  is  therefore  evident.  We  see  also 
by  heterical  induction  that  food  taken  into  the  6*omach  is  not  a  sine  qua  non 
to  the  life  of  the  foetus;  nor  is  the  respiration  of  atmosphere;  but  after'birtli 
both  these  things  by  ht)monical  induction  are  sine  quibus  non.  Nt)w  blood 
is  composed  of  fibrin©  and  serum,  and  eacii  of  these  has  been  analysed,  and 
they  are  found  to  be  isomeric,  i.  e.,  the  constituents  of  the  one  and  of  the 
ether  are,  not  only  similical  diilermtia,  but  also  by  weight  commensural  in- 
commensura.  It  has  been  found  also  that  if  the  blood  be  deprived  of  any 
one  of  its  constituents,  the  health  suft'ers;  eacn  one,  therefore,  by  homwnical 
induction  is  a  sine  qua  non.  We  can  prove  also  by  homonicai  induction  that 
light  is  a  sine  qua  non  of  the  growth  and  health*  of  reiretables;  for,  other 
things  being  equal,  they  will  not  dev^lone  in  dark  cellars  or  caves.  Most 
plants  contain  organic  acids  in  combination  with  bases  sucij  as  potash,  soda, 
lime  or  magnesia;  and  hence  it  has  been  concluded,  (but  it  is  onlv  probable 
and  not  an  induction)  that  an  alkalino  base  is  a  sihe  qua  lum  of  growth  of 
plants.  The  way  to  prove  it  is  to  make  an  experiment  and  have  all  other 
things,  found  in  th«  soil  and  atmosphere  where  the  plant  grows  well,  present 
excepting  these  ba.ses;  it  the  plant  will  tht-n  not  grow,  we  have  mad'e  an  ho- 
;nonical  induction. 

In  many  of  the  sterile  soils  on  the  coast  of  South  '  Anu-rica,  crops  of 
grain  will  not  grow  at  all;  but  it  guano  l>e  put  upon  those  soils,  they  then 
yield  abundant  crops;  her«  is  an  hommiical  induction  respecting  guano 
And  certain  soils,  which  are  entirely  barren,  may  be  rendered  fertile  by  put- 
ting quick  lime  upon  them.  Soils  also  destitute  of  alkalies  and  phosphates 
will  not  grow  certain  plants,  but  if  these  be  added,  the  plants  then  thrive 

•  upon  them ;  here  is  an  homonical  inducti(m.  Homonical  inductions  respect- 
ing the  hecessary  constituents  of  soils  for  raising  pl-iuts  may  readily  be  made 
by  comparing  a  productive  with  a  barren  soil.  We  take  the  following  analy- 
ses from  Dr.  Leibig's  agricultural  chemestry.  A,  repreHenis  the  surface  soil  • 
and  B  the  subsoil.    One  hundred  parts  contain : 

Kina''' ""''"'" ''^''"'"''''"'^^   • 95,m    95^180 

•  Protoxi^.i;*a*nd*p;;oxid;  of  iron  '.v.* '.  .'.V. V.V.V. JS^'      l^^ 

Peroxide  of  manganese ^'      ,       ^'^^ 

Lime  in  combination  with  silica '..'.'. on^s  '^^n a^;- 

Magnesia  in  combination  with  silica .' oVjlj       n  ml 

Potasaand8<a1a...  IJ™?-      "-^"^ 

O.oa5.      0.00} 


X 

16 

Phosphate  of  iron 0.198.      0.400 

Sulphuric  acid 0.002.  a  trace 

Cloriue 0.006.      0  001 

Humus  soluable  in  alkalies 1,000.      0.000 

Humu^  iusolualile  in  alkalie.s   0  502.      0.000 

100,000.   100,tKX) 

The  above  analysed  Roil  was  charactised  by  its  great   sterility.    White 

clover  could  not  be  made  to  grow  upon  it;  it,  therefore  furnishes  one  «)f  the 

cases  necessary   for   an    homonical    induction.      In    the  following    analysis 

we  have: 

A.  B. 

Silica  and  fine  seliciou>  sand 94,724.    97,340 

Alumiua 1,638       0.806 

Protoxide  and  peroxide  of  iron  with  maiiiranese 1,960.       1,201 

Lime 7 1,028.      0.095 

Magnesif". a  trace.  0.095 

Potash  and  soda * 0.077.       0.112 

Phosphoric  acid 0.024.      0.015 

CKpsum 0.010.  a  trace 

Clorine  of  the  >all 0  207.  a  trace 

Humus 0  512.      0.135 

100,000.  100,000 

Tiie  above  soil  produced  luxuriant  crops  of  lucerne  and  sainfoin  and 
all  other  plants  wh(»se  roots  penetrated  deeply  into  tlie  ground.  Now  from 
these  two  cases,  it  would  appear  that  in  those  plants  receiving  their  norish- 
ment  from  the  subsoil,  humus  was  a  sine  (|ua  non;  while  gypsum  is  inilieated 
as  a  ^ine  qua  non  in  the  surface  soil. 

W  we  taktt  muscular  tibrine,  which  contains  wuter,  and  let  it  be  ex- 
posed to  a  moist  atnmspiiere,  pulri fact  ion  takes  plac;;  but  if  the  fibrine  be 
dried  and  ihen  exposed  t**  a  diy  atmosphere,  no  such  result  takes  place. 
Hence  water  or  hydrogen,  is  a  sine  qua  non  of  the  putiMfaclion.  So  also 
yeast,  wheu  :;omplelely  dry,  possesses  no  power  to  produce  fermentation. 
Now  yeast  possesses  a  soluble  and  an  iusoluble  substance,  and  the  insoluble 
substance  may  be  thiowu  out  of  the  sine  quibii«  non  of  fermentation  by 
heterical  induction;  but  the  soluable  part  when  exposed  to  the  atmosphere 
produces  fermentation,  but  when  the  atmosphere  is  excluded  no  such  result 
takes  place.  An  aqueous  infusion  of  j'east  may  be  mixed  with  a  solution  of 
sugar  and  preserved  in  hermetrically  sealed  vessels  without  undergoing  the 
slightest  change,  but  if  exposed  to  the  atmosphere  fermentation  immediately 
begins.  Hence  the  soluble  part  of  yeast  and  the  atmosphere  are  proved  to 
be  sine  quibus  non  of  the  fermentation  which  ensues  in  such  cases.  Sever.al 
kinds  of  vegetable  fibre,  if  kept  secluded  from  oxygen  or  hydrogen,  do  n*>t 
decay,  but  when  oxygen  and  hydrogen  are  present  decay  commences;  each  of 

« 


i: 

those,  11)01  efnre,  is  a  sinf  qua  iion  of  :,ucl»  decay.  Oiker  bodies  do  not  decay 
wilhout  the  presence  of  a  free  alkali,  and  in  sueh  cases  alkali  by  homonical 
induction  is  u  sine  qua  non.  The  juice  of  grapes  expressed  under  a  receiver 
filled  with  mercury,  which  compUtHly  excluded  the  air,  <lid  not  ferment;  but 
when  ti»esmaiie.-5i  portion  of  air  Was  admitted  fermentation  immediately  be- 
gan. Animal  food  and  vegetables  may  bo  kepi  tor  years  wilhout  fermenta- 
tioti,  if  the  air  be  completely  excluded.  Wo  have  gone  far  enough  to  illus- 
trate the  manner  of  makiu','  and  the  u  iiity  of  homonical  inductions.  Any 
one  ol  the  cases  of  induction  given  above  may  be  stated  in  the  manner  of 
formulae  (3),  in  Chapter  II.  The  only  difficulty  in  arriving  at  C(mciusions, 
which  may  be  confidently  relied  up«»u,  lies  in  obtaining  the  precise  data 
needed;  if  these  can  be  had  our  coiiclusions  are  infallible. 

CPI AFTER  V. 

DIFFKKENTIAl,  INDUCTION  APPLIED. 

We  have  seen  iii  the   previous  book,    that    the    homonical  induction  of 
aggregations  only  proves  a  certain  aggregation    to  have  biien  a  sine  qua  nyn 
of  a  particular  eifect,  but  from  this  ca-^e  we   cannot    infer    by    raliocinali<.n 
that  this  particular  ag-:iegation  or  a  simile  of  it  must  be  a  sine  qua  non  of 
ail  similical  effects.     For,  as  there  shown,  two  aggregations,  as  agirreijations 
may  be  diftereatia,   and  yet  in  the  respect  of  lUe  grcgarium,  which  in  one  of 
the  aggregations  has  been  a  cause  of  the  given  effect,  the  two  may  be  inter  se 
snnilia;and    hence   the   necessity  of  differential    and   similicaf  inductions. 
This  matter  has  been  sufficiently   explained    heretofore.     Now    if  we   take  a 
view  of  the  elementary  gases,  we  will  i^r  by  diflerenial  induction,  that  ih(»se 
greiraria,  which  distinguish  g.isses  from  liquids  and  8<»lid8,  are  not  the  causal 
gregariaof  the  peculiar  action  of  any  gass   upon  another  substance;  for,  in 
these  disiinguisluni?   gregaria  gasses  all  agree.     By  ditferHutial  induction  we 
know,  that  the  peculiar  actirm  of  oxygen  upon  iron,  for  instance,  is  not  owing 
to  the  iiistinguisV.ing  gregaria  of  a  ga.-s;  for  if  it  were,  nitrogen   would  pro- 
duce upon  iron    asimilicttl    effect.     The   chemical  action  of  liquids   and    of 
feolids  may  be  treated  in   a  like  manner.     Each  element  possesses  a  chemical 
gregarium   sui   generis;  find    by   diiferenfial    induction    we  may  frequently 
draw  so  near  to  this   gregarium,   which    is   a  cause  of  certain  effects,    as    to 
leave  po  doubt  of  the  causal  gregarium,  tliongh  diflTerential  induction  does  not 
directly   determine  causes.     C<Huplete  differential    inductions  of  all  the  ele- 
ments wouhl    lay  the  foundations  upon    which  chemestry  might    be  made   a 
dedaciive  science;  whiclj  may,  as  we  hope,   b^  acoinplished   in  the  future. 
But  for  the  illustration  of  our  present  subject,   we  must  proceed   wi'h   such 
data  C.S  experimentalists  have  furnished.     And  we  may  commence,  not  with 
the  differential  induction  of  elements,  but  of  C(nnpounds.    On*;  element  may 
Bor  RX'^rt  .some  peeuli.'r  force  wifimut  the  presence  of  another  or  others,  with 


18 

which  it  is  compounded,  and  then  this  peculiar  compound  is  the  sine  qua 
no.i  of  a  given  ei!ect.  This  is  owing  to  the  circumstance,  that  compounds 
possess  capacial  gregaria,  wliich,  with  reference  to  the  gregaria  of  either  of 
the  elements  entering  into  them,  are  diflferentia.  We  may  begin  our  illustra- 
tions, therefore,  by  difierentiating  compounds.  And  as  by  analysing  com- 
posite substances,  they  are  resolved  into  simple  differential  compounds,  we 
may  assume,  for  the  sake  of  illustration,  that  each  of  the  simpler  compounds, 
into  which  a  composite  substance  can  be  resolved,  exerts  its  gregaria  unim- 
peded when  in  the  more  complex  substance. 

Now  according  to  Brandes,  rhubarb  contains:  Rhubarbic  acid;  Galic 
acid;  Tannin;  Sugar;  Colouring  extractive;  Starch;  Gummy  extractive; 
Pectic  acid;  Malate  of  lime;  Gallate  of  lime;  Oxalate  of  lime;  Sulphate  of 
potta.ssa;  Cloride  of  pottasium;  Silica;  Phosphate  of  lime;  Oxide  of  iron ; 
Lignin;  Water.  And  if  by  differential  induction  we  are  iu  search  of  the 
purgative  ingredient  of  rhubarb,  we  may  differentiate  water  by  a  comparison 
of  rhubarb  wit'^  the  juice  of  the  sugar  cane,  both  contain  water,  they  agree 
iit  tins  respect;  we  may  ditferentiate  lignin  by  a  comparison  with  almost  any 
woody  fibre;  the  oxide  of  iron  and  silica  by  a  comparison  with  the  water 
from  wells  and  thermal  springs;  phosphate  of  lime  by  a  comparison  with 
bone  dust  cloride  of  pottassium  by  a  comparison  with  sea-water;  the  sul- 
phate of  pottassa  by  a  comparison  with  potashes;  the  oxalate  of  lime  by  a 
comparison  with  wood-sorrel;  Gallate  of  lime  by  a  comparison  with  gall- 
nuts;  the  malate  of  lime  by  comparison  with  vegetables  such  as  the  house- 
leek  ;  Tannin  by  a  comparison  with  the  bark  of  oaks;  sugar  and  starch  by 
comparisons  with  wheat  flour  and  maple  saps  &c.  As  the  above  compounds 
can  be  separated,  we  could  use  heterical  and  homonical  inductions,  and  that 
is  the  better  way,  for,  it  relieves  us 'from  making  an  assumption  at  the  outset 
which  may  not  be  true;  but  for  the  sake  of  illustration  we  hare  used  difi'er- 
cnlial  induction.  If  we  wish  to  find  by  diflTerential  induction  in  what  the 
poisonous  gregaria  of  morphia  consist,  we  may  analyze  this  compound  and 
wc  find  it  to  contain  carbon,  hydrogen,  oxygen  and  azote.  We  can  diflTer 
entiate  the  carbon  by  the  comparison  with  fat  beef  or  pork;  the  hydrogen 
and  oxygen  by  a  comparison  with  water;  and  the  azote  by  a  comparison  with 
gluten  or  indigo.  And  hence  it  appears  that  neither  of  these  elements  per  se 
is  the  cause  of  the  poisonous  eflfects  of  morphia,  but  that  the  causal  gregaria 
arise  from  the  compound.  There  is  in  this  induction,  however,  the  same  as- 
sumption, which  we  made,  when  treating  of  rhubarb,  and  though,  we  think, 
we  are  at  liberty  to  make  such  assumption  for  the  sake  of  conveying  to  the 
reader's  mind  the  application  of  a  principle  yet  in  the  actual  search  after 
truth,  such  assumption  is  inadmissable.  We  must  deal  with  morphia,  there- 
fore, not  by  its  ingredients,  but  by  its  gregaria. 

Now  morphia  among  otherj  coontains  the  following  gregaria. 


19 

MoupiiiA.— It  is  fusible  at  niodctsite  liiaf ;  it  burns  with  a  red  and  very 
smoky  flume;  it  is  s«)luble  in  80   parts  of  boilino:   auliydrous   alcohol;    it  is 
soluble  lu  500  parts  «^f  boilin!i  v\'uier;   if  is  insoluble  in  cohl  water;   it  is  in 
soluble  in  ether;  it  is  iusMJuble  in  oil;  it  is  insoluble  in  chloroform ;  it  foim^ 
salts  with  acids. 

We  will  assume  that  the  above  data  are  correct,  though  chemists  difli  r 

respecting  some  of  the  gregaria.    Tjie  following  are  some  of  the  gregaria  of 

starch  a  uon-poisouous  substance: 

Stauch-  It  is  insoluble  in  cold  water;  it  is  insoluble  in  cold  alco- 
hol; it  is  insoluble  in  ether;  it  is  insoluble  in  oil. 

The  following  are  si.me  of  the  gregaria  ot  resin  a  nou-poisonous 
substance. 

KEsiN.—It  is  fusible  at  moderal'  heat;  it  is  insoluble  in  watcrr;  it  is 
translucent;  it  burns  with  bright  flame  and  very  much  .smoke. 

Now,  if  we  compare  morphia  with  these  last  two  non-poisonous  sub- 
.stances  we  will  see  that  several  ol  their  gregaria  are  inter  se  similia;  thes.- 
gregarin,  tlierefore,  may  be  difterentiated  from  the  poisonous  gregaria  con- 
tained in  morphia,  and  further  investigation  must  be  had.  , 

Again;  wc  know  thai  common  salt,  cloride  of  sodium,  is  an  antiseptic 
and  wlien  applied  to  fresh  flesh  it  i)revents  decay;  we  may  inquire  inerefore, 
r.?specting  the  caustil  gregarium  of  this  phenomenon.  Now  among  the  gre- 
garia of  common  salt  are  the  followin«! : 

Salt.— It  has  a  white  color;    it  has  a  saline  taste;    it   undergoes   but 
little  change  in  a  dry  atmosphere;  it  dissolves  in  water;  U  dissolves  but  liitl. 
in  alcohol ;  it  melts  by  iieal ;  it  is  decomposed  by  carbonate  of  pota^.-a. 

With  common  salt  we  may  compare  Eps<»m  salts,  sulphate  of  mag- 
nesia, wliich  among  others  contains  the  following  gregaria: 

ErsoM  Salts.— It  has  a  white  coloi:,  it  has  a  saline  taste,  it  undergoes 
but  little  change  in  a  dry  atmospliere,  it  dissolves  in  water,  it  dissolves  but 
little  in  alcohol,  it  melts  by  heat,  it  is  decomposed  by  carbonate  of    potas.sa. 

Now  the  similia  may  be  difterentiated  fron»  the  causal  gregaria  and 
the  matter  must  then  be  further  inquired  into.  We  have  gone  far  enough 
with  our  illustrations  to  see  that  true  difl'erential  inductions  can  be  obtained 
only  from  the  comparison  of  gregaria.  And  any  one  who  will  examine  the 
matter,  will  find,  that  in  what  Bacon  would  call  the  history  of  substances, 
chemical  science  is  yet  very  defective.  We  need  further  experiments  to  be 
made  under  the  guidance  iW  a  true  philosophy. 

CHAPTEli  VI. 

8IMILICAT-   INDt'CTION  APPIJED. 

As  helerical  induction  clears  the  way  for  homonical  induction,  so 
differential  induction  prepares  the  way  for  similical  induction.  And  both 
difl"erential  and  similical  inductions  to  be  satisfactory  must  be  based  upon  a 
great  number  of  gregaria,  which   requires  a  very  extensive  knowledge   of 


20 

subitanciis.  We  do  uo{  propose  to  give  complete  and  whcdly  satisfactory  in- 
ductions respecting  the  causal  gregaria  of  effects;  for  that  would  require  a 
different  kind  of  treatise  from  the  one  upon  which  we  are  now  engaged,  but 
we  merely  propose  to  illustrate  the  principles  of  induction  and  let  scientific 
men,  each  one  in  his  own  special  department,  make  the  application  with  full 
data  to  particular  subjects.  Now  if  we  wish  to  find  the  poisonous  gregarium 
or  gregaria  contained  in  Muriatic  or  Sulphuric  acid,  we  may  examine  their 
gregaria  in  the  following  manner.  Some  of  the  gregaria  of  Muriatic  acid 
are  as  folio ws^: 

•  MuHiATic  AciD.-^It  is  a  Colorless  liquid,  it  has  a  sour  taste,  it  corrodes 
animal  tissues,  it  is  incompatable  with  metalic  oxides,  it  is  IncompalaMe  with 
alkidies,  it  redens  litmus  paper,  it  has  a  strong  }»t!inily  for  water. 

The  following  are  some  of  the  gregaria  ol  Sulpliuric  acid: 

Sui.i'HURrc  Acid.— It  is  a  colorless  liquid,  it  has  a  sour  taste,  it  cor- 
rodes aniniul  tissues,  it  is  incompatable  with  metalic  oxides,  it  is  incompata- 
ble with  alkalies  it  redens  litmus  pa[)(?r,  it  has  a  strong  affinity  for  water. 

For  tlie  purpose  of  dillereiitial   induction   we  may  compare  with  the 

above  acids  th'i  acetic  acid  of  commerce,  u  substance  which  may  be  taken  in 

large  quantities  without  poisonous  effects.    Some  of  the  gregaria  of  actttic 

acid  are  as  follows: 

Acetic  Acid.— It  is  a  colorless  liquid,  it  has  a  sour  taste,  it  is  incmn- 
[laiable  with  metalic  oxides,  it  is  incompatable  with  alkalies,  it  redens  litmus 
paper,  it  has  a  strong  affinity  for  water. 

Now  if  we  differentiate  the  similical  gregarin  of  acetic  acid  from  the 
poisonous  gregaria  Cimtained  in  sulphuric  and  muriatic  acids,  we  find  the 
latter  two  acids  to  agree  in  their  gregaria  of  corroding  animal  tissues.  And 
b}'  similical  induction  this  corroding  gregarium  is  a  causal  gregarium  of  the 
poisonous  effects;  it  produces  the  direct  destruction  of  thworgans  with  which 
it  comes  in  contact,  and  hence  death  ensues. 

Tiiero  is  another  class  of  poisons,  which  do  not  corrode  or  immedi- 
ately destroy  the  organs  with  which  they  come  in  contact,  but  by  their  action 
they  render  the  tissues  incapable  of  performing  their  functions.  Of  these  we 
ma}'  compare  the  salts  of  lead  and  of  copper. 

The  following  are  some  of  the  gregaria  of  the  carbonate  of  lead : 

Carbonate  of  Lead. — It  is  a  white  solid,  it  is  loswluble  in  water, 
it  is  soluble  in  acid,  it  is  soluble  in  alkali,  it  enters  into  firm  combination 
witii  animal  tissues. 

The  following  are  some  of  the  gregaria  of  what  is  commonly  called 
vcrdegris,  the  carbonate  of  copper: 

Carbonate  op  Copper. — It  is  a  green  solid,  it  is  iusoluable  in  water, 
it  is  soluble  in  acid;  it  is  soluble  in  alkali,  it  enters  into  firm  combination 
with  an!mal  tissftes. 

For  purposes  of  differential  induction  we  may  compare  pure  indigo 
with  the  above : 


21 

Indigo.— It  is  a  blue  solij,  it  is  insolubk*  in  water,  it  is  soluble  in 
acid,  it  is  sv>luble  in  iilkali. 

After  differentiating  we  find  carbonate  of  lead  and  copper  to  agree  in 
the  gregarinm  of  entering  into  firm  combination  with  animal  tissues;  and 
vital  organs  thus  rendered  calous  and  intlexible  can  not,  of  course,  perform 
their  functions,  and  hence  death  must  ensue.  We  do  not,  however,  give  the 
above  as  satisfactory  inductions;  the  dat;;  are  insufficient  ;!nd  some  of  tlieni 
may  not  be  correct.  Chemists  have  not  been  fymiliar  with  the  inductive  pro- 
cesses and  they  htwe  not  looked  for  data  in  view  of  making  diJfereutial  and 
similical  inductions,  and  hence  they  liave  not  furnislied  us  with  the  reqwisitc 
ground- works. 

As  another  case  to  illustrate  the  principle  of  similical  induction  we 
may  inquire  into  the  causes  of  the  doub)'^  refraction  of  light.  Some  of  the 
gregaria  of  the  carbonate  of  lead,  winch  substance  causes  double  refraction, 
are  the  following: 

Carbonate  op  Lead. —It  is  a  transparent  snbsrance,  it  is  of  crv«taline 
structure,  jts  crystals  nvv,  of  tlie  rhombohedral  torm,  it  is  insoluble  iu  wnln 
It  is  soluble  in  acid,  it  is  soluble  in  alkali. 

The  following  are  some  of  the  gregaria  of  Iceland  spar,  another  sub- 
stance causing  double  refraction : 

IcEi^\ND  SpAii.— If  is  a  transparent  substance,  it  is  of  crystaline  struc- 
ture its  crystals  arc  of  the  rhombohedral  form,  it- is  insoluble  hi  water,  it  i^ 
soluble  in  acid 

The  following  are  some  of  the  gregaria  of  one  species  "of  diamond, 
which  causes  double  refraction: 

Diamond.— Jt  is  a  transparent  substance,  it  is  of  crvslnline  structure 
lis  crystals  are  of  the  rhombohedral  from,  it  is  ins.duble  in  water,  it  is  soluble' 
in  acid. 

Witli  the  foregoing  double  refracting  substances  we  may  compare   the 

following  substances,  which  do  not  refract  light  in  that  manner.    The  follow  - 

ing  are  some  of  the  gregaria  of   a  species  of   diamond  which  causes  single 
refraction : 

Diamond.— It  is  a  transparent  substance,  it  is  of  crystaline  structure. 
Its  crystals  are  of  the  octohedrai  form,  it  is  insoluble  in  Water,  it  is  soluble 
in  acid.  ,  i*wt 

^    The  ftdlowing  are  some  of  the  gregaria  of  pure  rock  salt : 

Rock  Salt.— It  is  a  transparent  substance,  if  is  of  crystaline  structure, 
Its  crystals  are  either  of  the  cubical  or  octohedrai  form  but  sometimes  pris- 
matic, It  IS  insoluble  in  water,  it  is  soluble  in  acid. 

The  following  are  some  of  the  gregaria  of  pure  borax: 
Borax.— It  is  a  transparent  substance,  it  is  of   a  crystaline  &lruchire 
Its  crystals  are  either  of  the  prismatic  or  octohedrai  form.  "  • 

Now  after  using  differential  inductions  we  find  the  substances  causing 
double  refraction  to  agree  in  having  their  structure  made  upot  rhombohedral 


22 

crystals.  And  from  this  it  would  appear  that  the  form  of  the  crystal  causes 
double  refraction  ;  but  our  data  are  again  insufficient  for  a  satisfactory  iuduc- 
ti(»n.  There  are  fourteen  difTerent  forms  of  crystals  entering  into  the  struc- 
ture of  diamonds  and  onl}'  two  of  which,  the  oclohedra  and  cube,  so  far  as 
we  can  learn,  cause  single  refraction.  The  subject  needs  further  examina- 
tion with  more  full  and  m»re  certainly  correct  data.  Fesnel  explains,  deduc- 
tively, double  refraction  by  assuming  that  the  ether  in  double  refracting  sub- 
stances is  not  equally  elastic  in  all  directions.  This  is,  of  course,  merely  aa 
hypothesis,  and  the  evidvnce  by  which  it  can  be  inductively  proven  is  not 
furnished  by  double  refracting  substances.  Newton  concluded,  probably 
per  euuinerationem  simplicem,  that  c«mbusiibility  was  in  some  way  a  cause 
of  retraction  and  then  reasoning  a  posteriori  he  conjectured  that  water  and 
the  diamond  would  be  found  to  contain  combustible  elements;  and  his  3on- 
jecture  has  been  verified.  But  we  have  gous  far  enough  to  illustrate  the 
principle  of  similical  induction. 

CHAPTBli  VII. 

INCOMMENSURAL  INDUCTION  APPLIED. 

We  have  seen,  heretofore,  that  there  are  three  cases  of  incommensural 
inducti'^i,  having  reterence  to  three 'kinds  of  relations  between  the  causes 
and  their  ef!*ects.  And  if  we  commcRce  our  illustrations  with  incommen- 
sural quantities  of  certain  objects,  which  we  are  examining  for  the  purpose 
of  determining  their  relations  to  certain  incommensural  effects,  we  will  soon 
see  the  utilit}^  of  this  method  from  the  dailj'  necessities  of  life.  On  making 
our  fii*te9  in  the  stove,  we  need  but  admit  a  small  current  of  air  and  then  a 
greater  one  to  convince  us,  by  incommensural  induction,  that  the  atmosphere 
is  connected,  iu  som«  manner  through  causation,  with  the  combustion  going 
on  in  the  stove.  And  we  need  but  increase  the  inhalation  of  oxygen  into  our 
lungs  to  find  out,  that  certain  phenomenal  effects  in  our  system  are  depedent 
upon  the  respiration  of  this  gass.  'The  incommensural  quantities  of  the 
sun's  rays  falling  vertically  and  obliquely  upon  equal  areas  in  different  lati- 
tudes, must  also  convince  u^  of  their  relations  through  causation  with  the 
earth's  temberature  and  vegetation.  And  in  every  branch  of  agriculture, 
horticulture  and  floral  training,  the  case  of  incommensural  inductions  tr.om 
the  relations  of  quautity  may  be  made  by  a  little  ingenuity.  I  extract  the 
following  facts  from  Prof.  Liebig's  agricultural  chemistry:  "The  employ- 
ment of  animal  manure  in  the  cultivation  of  grain  and  the  vegetables  which 
serve  for  fodder  to  cattle,  is  the  most  convincing  proof  that  the  nitrogen  of 
vegetables  is  derived  from  ammonia.  The  quantity  of  gluteu  in  wheat,  rye 
and  barley,  is  vory  different;  these  kinds  of  grain  also,  even  when  ripe,  con- 
lain  this  compound  of  nitrogen  in  very  different  proportions.  Proust  found 
Fi'iuch  wheat  to  contain  12.5  per  cent,  of   gluten;    Vogel   found  that  the 


I 


23 

BurvariaQ  contuiued  34.  per  cent;  Davy  obtained  19.  per   cent,  from    winter 
and  24.  from  summer  wlieat;  from  Sicilian  21.  and  from  Barbary    wheat   19. 
per  cent.    The  meal  of  Alsace  wheat  contains,  according  to   Bous^ingault 
17.3  per  cent,  of  gluten;  that  of  wheat  grown  in  the  'Jardin  dcs  Plautes'  2G.7 
and  that  of  winter  wheat  3.33  per  cent.    Such  great  differences  must   by  ow 
inoj  to  some  pause,  and  this  we  find   in  the  diflerent  methods  of  cultivation. 
An  increase  of  animal  manure  give.s  rise  not  «nly  to  an  increase  in  the  num- 
ber of  seeds,  but  also  to  a  most  remarkable  difiereuce  in   the  projHution  of 
the  substances  containing  nitrogen,  such   as  tlie  gluten  which  they  contain. 
*    *    *    *    ^    One  hundred  parts  of  wheat  grown  on  a  soil   manured   with 
cow-dung  (a  manure  containing  the  smallest  quantity  of   nitrogen)  atfordtd 
only  11.95  parts  of  gluten  and  64.34  p^rts  of   amylin   or  starch;    while   the 
same  quantity  grown  on  a  ^il  manured  with  human  urine,  yielded  the  max- 
imum of  gluten,  namely  35.1  per  cent.    Putrified  urine  contains  nitrogen   in 
the  forms  of  carbonate,  phosphate  and  lactate  of   aramrtnia  and   in  no  Other 
form  than  that  of  ammonical  salts."    :^'ovv,  in  the  above  facts,  granting  the 
soils  and  atmospheres  to  have  been  in  all  other  respects  inter  se  similical  and 
commewural,  there  is  a  fair  incommensural  induction  respecting  ammonia. 
In  another  case  of  incommensural  induction,  we  have  seen  that,  ceteris 
paribus,  the  spaces  between  an  object  contaiijing  causal  ^fregaria  and  the  itcnm- 
meusural  effects  are  incommensural;  and  we  will  now  pioceed  to  give  a  few 
simple  illustrations  of  this  case.     It  is  said  thatGalil«o,  perceiving  that  the 
chandeliers  suspended  in  a  church,  when  se4  in  motion,  vibrated  long  and 
with  uniformity,  was  led  by  these  phenomena  to  invent  the  pendulum.     With 
this  instrument  a  great  many  persons  have  since  experimented;  and  the  phe- 
nomena(^f  it«  vibrations  are  found  to  be  incommensura  in  diflerent  latitudes 
and  localities.    A  pendulum  of  about  39  inches,  wliich  vibrates  seconds  in 
the  latitude  of  New  York,  will  not  vibrate  sixty  times  in  an  iiour  of  corn- 
mensural  time  on  the  equator;  and  there  is  a  marked  difference  in  the  time 
of  the  vibrations  of  tlie  same  pendulum  iri  the  valleys  of  the  Amazon  and  on 
the  liigh  peaks  of  the  Andes.    The  farther  you    remove  the  pendulum  from 
the  earth's  center  of  gravity,  the  fewer  will  be  its  liibratlons,  ceteris  paribus 
And  hence  we  learn  from  these  incommensural  relations  of  spaces   between 
the  earth  and  the  incommensural  effects,  that  the  earth  contains  causal  gre- 
garia  of  these  phenomena.  Again  :  The  surveyor,from  the  incommensural  illa- 
tions of  spaces  between  his  compass  and  a  c  riain  hill   and  incommen.>ural 
variations  of  the  needle  from  the  true  meridian,  concludes  that  the  hill  pos- 
sesses causal  gregaria  of  these  variations.    The  incommensural   relations  of 
the  spaces,  between  the  moon  and  the  waters  on  different  parts  of   our  earth, 
and  the  tides,  furnish  also  the  data  from  which  to  make  incommensural   in- 
ductions; and  although  the  tides,  on  the  opposite  side  of  tj^e  earth  from  the 
moon,  might  seem  at  first  thought,  to  destroy  the  force  of  these  data,  yet  when 


24 

wc  reflect  that  the  earth  is  interposed  between  the  moon  and  those  tides,  the 
(lata  remain  in  their  validity.  The  reader  will  understand  that  in  incom- 
mensural induction  from  incommensural  relations  of  space,  we  are  seeking 
merely  for  some  object  which  contains  causal  gregaria  of  the  incommensural 
ottectsj  no  matter  what  may  be  the  characters,  in  other  respects,  of  the  in- 
coaimensural  effects  in  their  relations  inter  se.  Thus:  if  we  try  the  posi- 
tively electrified  end  of  a  cylinder  with  the  knob  of  a  charged  Leyderi  jar 
;uid  find  the  cylinder  to  b^  repelled,  and  then  we  try  the  negative  pole  of  the 
cylinder  and  find  phenomena  of  an  opposite  character,  by  incommensural 
relations  of  sp:jcc  and  the  incommensural  effects  of  each  kind  inter  se,  i.  e., 
mcommensural  similia  b(»th  these  sets  of  phenomena,  though  inter  se  differ- 
entia, are  proved  to  have  a  dependence  upon  the  knob  of  the  jar,  i.  e.,  the 
knub  contains  causal  gregaria  of  both  lhe.se  sets  of  phenomena. 

We  will  nww  give  a  few  illuitralions  of  the  case  in  which  incommen- 
sural inductions  can  be  obtained  from  incommensural  relations  <tf  times.  If 
we  should  find  find  b}-  tne  side  of  a  mountain  a  ledge  of  iron  ore  which  had 
been  uncovered  for  but  a  quarter  of  a  century,  and  on  the  same  mountain  we 
should  find  ore,  whicli  liad  been  bare  lor  several  centuries,  and  we  shmild 
make  com|>arisons  between  the  two,  we  would  be  able  to  drjuv,  from  the  in- 
commensural eftV'cts  perceived  in  the  ores,  conclusive  incommensural  induc- 
tions of  the  cause  from  the  incommensural  relations  of  times,  had  we  never 
thought  of  the  cause  before.  For,  granting  that  all  other  things  are  similical 
and  commensural  in  the  two  sets  oC  phenomena  excepting  the  times  of  ex- 
posure to  the  atmo«pher3,  and  ihe  (luantities  of  atmosphere  being  commen- 
sura  in  commensural  limes,  no  object  whatever,  excepting  the  atmosphere 
could  have  incommensurated  the  effects  witnessed  in  the  oxyilized  ores.  A 
hound  by  instinct  .as  we  call  it,  makes  a  kir.d  of  inverse  incommensural  in- 
duction concerning  incommensural  effects  from  incommensural  relations  of 
lime,  or  we,  ar  least,  may  make  it  for  him,  when  he  is  pursuing  the  trail  of  a 
deer.  Each  tread  of  the  deer  deposits  in  the  soil  a  certain  effect,  and  these 
effects  immediately  after  the  treads  in  similical  soils  are,  no  doubt,  very  nearl}- 
commensural  inter  se,  and  which  the  atmosi)here  with  the  soil  cftmences  to 
diminish,  leaving  at  incommensural  intervals  of  time  from  the  point  from 
which  they  were  made  incommensural  effects.  When  the  hound,  therefore, 
strikes  a  rather  old  track,  not  having  a  scientific  kpowledgeof  the  relalions-of 
time,  space  and  velocity,  and  no  means,  in  the  present  case,  of  judging  of  the 
last,  he  is  not  very  animated  in  the  pursuit,  not  expecting  to  find  the  deer  for 
some  time,  although  it  may  have  lain  down  within  forty  rods  from  the  point 
where  he  struck  the  trail.  But  as  he  moves  on,  he  perceives  incommensura; 
he  then  increases  his  speed,  and  finding  the  degrees  of  the  incommensura,  or 
differences,  to  increase  rapidl}',  he  becomes  warm  and  boisterous,  proclaim- 
ing as  he  goes  the  state  of  his  expectations,  in  relation  to  time  of  coming  up 


25 

■with  the  cause  of  these  iucommeasural  phenomena.  Should  a  man  buy  two 
pair  of  boots  inter  se  sirailia,  and  walk  in  one  pair  over  a  given  road  for 
six  hours  a  day  for  two  months,  and  then  in  like  place  and  manner  walk  in 
tiie  second  pair  for  four  months,  and  observe  the  incommensural  effects  and 
times,  he  would  not  hesitate  to  make  an  incommensural  induction.  We  need 
go  no  further  with  illustrations. 

It  must  hare  been  noticed  bv  the  reader  that  when  we  are  cousiderin"- 
incommensural  effects  inter  se,  our  comparisons  havj  reft?rence  to  nolhiuj^^ 
else  than  quantity,  i.  e.,  the  effects  inter  se  are  quantltively  incommensura. 
It  will  be  noticed  too,  that  drops  of  water  inter  se  commensural  falliuirat  in- 
tervals  of  one  second  for  one  year,  and  commensural  drops  falling  in  like 
manner  for  half  a  year,  produce  incommensural  effects  from  the  incommen- 
sural quantities  of  cause.  And  when  a:i  aa:grogation  exerts  from  itself  in- 
fluences through  space,  as  iu  the  radiation  of  heat  for  instance,  an  object 
nearer  and  one  more  remote  from  the  focus  of  influence,  providing  the  objects 
be  inter  se  commeusura,  Mill  receive  incommensural  quantities  ol  the 
influence  in  commensural  times.  And  hence,  laying  aside  the  interference  of 
cause*,  the  quantities  of  causes  and  effects  are  prop(»rtional.  The  assertion 
that  ettects -are  proportional  to  their  causes,  however,  must  not  be  understood 
to  mean  that  such  is  the  case  absolutely  and  without  limit,  as  we  will  better 
understand  hereafter. 

CHAPTER  VIII. 

rOMMENSUP.AL   INDCCTION   ArPIJED. 

Commensural  like  incomiuensural  induction  deals  only  with  effects, 
which  are  inter  se  similia.  And  we  take  a  certain  case,  in  which  we  have 
heretofore  determined  a  certain  object  to  contain  causal  gregaria  of  a  specific 
effect,  and  having  determined  the  time  space  and  quantity  in  this  case,  we 
endeavor  to  ascertain  what  objects,  over  which  we  may  have  no  control, con 
tain  similical  gregaria  with  reference  to  such  similical  effects,  from  the  rela- 
tions of  the  time,  space  and  quantity  of  the  case  in  which  the  object  is  under 
our  control  to  the  time,  space  and  quantity  in  other  caees  of  similical  effects 
in  which  the  objects  containing  causal  gregaria  are  not  under  our  control. 
And  in  commensural  as  in  incommensural  induction  there  are  three  cases. 
Let  us  commence  oi.ir  siiuple  illustrations  with  the  commensural  relations  of 
space.  Suppose,  for  instance,  we  had  made  experiments  with  a  certain  ivory 
ball  and  found  that  when  we  let  this  ball  fall  forty  feet  upon  iron  of  a  smooth 
surface,  it  rebounded  a  certain  number  of  fe«l;  when  we  let  it  fail  upon 
marble  in  like  manner  it  rebounded  a  certain  other  number;  and  when  upon 
brass  in  like  manner  a  certain  other  and  so  on :  and  in  all  these  experiments 
vfd  will  suppose  the  plates  of  the  different  metals  and  minerals  with  which 
we  experimented  to  be  quite  thick  and  placed  upon  solid  granite  rock.    The 


26 

rebounding  of  the  ball  is  the  elFoct  in  the  ball  witnessed  by  us,  of  which  the 
space througli  which  it  rebounds  is  the  quantum:  and  some  of  the  causal 
gregaria  of  this  eff'ect  are  in  the  ball  and  the  others  are  in  the  objects  -upon 
which  it  fell.  Suppose  now,  after  this,  we  find  a  mass  of  metal,  of  a  'kind 
unknown  to  us,  underlain  with  granite  and  we  let  the  same  ivory  ball  fall 
upon  its  smooth  surface  forty  feet  and  observe  iti  rebounding,  and  we  find 
this  effect  to  be  commensural  with  that  obtained  when  it  wa's  let  fall  upon 
marble;  then  as  the  ball  is  the  same  and  other  things  are  equal,  the  commen- 
sural relations  of  the  spaces  fallen  through  by  the  ball  in  the  two  cases  to 
the  commensural  effects,  convince  us  by  commensural  induction,  that  this 
new  metal  contains,  in  the  respect  to  these  similical  and  commensural  eff'ects 
.similical  and  commensural  causal  gregaria  witli  those  contamed  in  marble.' 
And  should  this  new  metal  be  so  situated  that,  we  could  not  approach  to  it  so 
as  to  examine  it  closely  with  our  eyes  or  feel  it  with  our  hands  and  the  ball 
used  bean  heterical  one,  but  similical  and  commensural  with  the  first,  the 
result  would  be  the  same.  Again:  Suppose  we  make  experiments  with  a 
certain  magnet  and  find  that  if  we  attach  the  one  end  of  a  small  string  to  the 
north  pole  of  a  magnetic  needle  placed  at  a  certain  distance  from  the  magnet 
and  the  other  end  to  a  weight,  which  the  magnet,  when  the  magnetic  needle 
is  at  right  angles  to  it,  will  just  be  able  to  draw  on  a  certain  surface  until  the 
needle  points  directly  towards  the  magnet,  this  drawing  of  the  weight  then 
mny  be  taken  as  the  (luautum  of  the  eff-rct:  it  we  now  take  a  piece  of  ©re 
and  situate  the  needle  with  weiglit  attached  on  the  same  surface  as  'before 
and  a  commensural  effect  be  produced,  we  conclude  by  commensural  induc- 
tion, having  our  eye  on  the  commensural  relatiors  of  the  spaces  in  the  two 
cases  and  times  being  supposed  commensural,  that  the  magnet  and  ore  con- 
tain similical  and  commensural  causal  gregaria.  Again  ;  if  we  make  a  fire 
in  a  stove  and  hold  a  thermometer  at  a  certain  distance  from  it  and  read  the 
degrees  to  which  the  mercury  rises  in  a  given  lime,  this  rising  of  the  mer- 
cury  will  be  the  quantum  of  the  effects;  if  then  we  go  to  a  heap  of  quick 
lime  witJi  water  thrown  upon  it  and  covered  up  with  earth,  and  we  place  the 
thermometer  at  a  commensural  distance  from  it  and  find  the  quanta  of  eff-ects 
t )  be  inter  se  commensural,  we  conclude  that  the  heap  contains  similical  and 
commensural  gregaria,  respecting  such  eftecls,  with  the  stove. 

Secoiid  Case.-ir  we  take  the  down  of  the  goose  and  find  that  a  certain 
quantity  will  be  attracted  through  a  certain  space  in  a  given  time  by  the 
prime  conductor  of  an  electrical  machine,  and  we  then  take  a  commensural 
quantify  of  the  down  of  the  swan  and  find  it  to  be  attracted  through  the  same 
space  in  a  commensural  time,  we  conclude  the  latter  substance  to  contain 
similical  and  commensural  causal  gregaria  with  the  former.  If  a  weight  be 
attached  to  a  baloon  and  the  baloon  then  ascend  a  given  distance  in  a  c*ertain 
time,  and  we  then  attach  the  same  weight  to  another  commensural  baloon 


r27 


and  111.-  secoiul  one  make  the  sm\c  distance  in  a  commeiisural  time,  the   two 
bulootis  contain  similical  and  coniuunsura  j^regaiiu. 

.   Tiiird  Ciise.— If    we  charge  a  certain   Levilon  Jar  to   its  capacity   and 
measure  tlie  space  throu-h  wliich  a  spark  from  tlie  knob   can    be   miide    to 
pass  so  as  to  ignite  sulphuric  elher  and  then  wu  dischar«re  a  spark  of  the  jar 
commensuraily  ciiarged  thr(.ugh  tiie  same  space  into  ellier  of    alcohol    and 
find  commensural  elfects,  times  being  equal,  we  conclude  tlie  two  ethers    to 
contain  similical  and  c  Mumensurul   causal    gregaria  with   reference  to   such 
effects.     VV(.  need  not  illustrate  farther.     If  ihe  reader  will  bear  in  mind  that 
all  elfects  arc  produced  by  heterical  causal  gregaria,  som«i  of   whicii   are    in 
the   objects   in    which    we  witness  the   effect,  and    some   in    another  object, 
numerous  examples,  from  which  commensural  inductions  can  be  made,  will 
suggest  them.-elves  to  his  own  mind.     And  it  is  evident   that    if    we  can  not 
always  find  commensural  relations,  we  may  yet  make  our  inductions  iu  many 
cases  by  tlie  commensural   relations  ot    mathematical   ratios.     By  taking    a 
piece  of  iron,  for  instance,  to  incomiiien^uhal  distances  from  the  earth's  sup- 
face  and  rinding  the  ratios  of  its  Aveigiilsand  distances,  we  rind  that   grarity 
varies  inversely  as  the  square  of  the  distance;  we  tiiid   also  that   the   matter 
•  tends  to  move  in  straight  lines  with  a  force  equal  to    its   we4ght    multiplied 
into  its  velocity;  and  tliereforc,  near  the  surface  of  t!ie  earth  if  we  pioject    a 
stone  of  a  certain  weight  iu  a  horizontal  direction  with  a  given  velocity,  we 
can  calculate  the  <Hstance  it  will  make  through  space    in  tiiiiling  to  the  earth 
by  gravity.     Now  if  we  contemi>late  the  n7oon  and  find  its  ratios  to  be  com- 
mensural witii  the  ratios  of  our  experiment  with  the  stone,  we   conclude    by 
commmensural  induction,  that   the   moon  and   the   stone   C(mtain   similical 
causal  gregaria.     In  this  manner  Xewton  extended  gravity  to   the  moon,  aud 
it  has  since  been  exientled  to  other  heavenly  bodies;    and  it  is  supposed,  by 
iuductio  per  enumeraiioaem  simplicem,  to  exi.^t  throughout  the  universe. 

CHAPTER  IX. 

THE  DENOMINATK  UNIT. 

Tho.se  Avho  have  mastered  the  principles  of  books  I  and  II,  and  of  the  pre- 
vious chapters  in  this  hook,  (whicli  in  the  last  four  chapters  we  have  emleav- 
ored  to  render  more  easy  for  the  understanding  by  giving  simple  illustrations 
with  sensuous  objects)  vrill  be  able  now  to  proceed  furtner  with  us  in  our 
still  deeper  inquiries  into  nature's  piocesses.  In  our  previous  inquiries,  ex 
cept  in  similical  and  differential  inductions,  we  have  dealt  mostly  with  ag- 
gregations, and  have  not  given  much  ot  our  attention  to  gregaria,  from  whicli 
only,  tho.se  relations,  which  are  called  the  laws  of  nature,  can  be  evolved 
And  wo  have  seen,  heretofore,  that  homon  per  se  makes  no  part  of  our  knowl- 
edge, but  tnat  we  gain  our  knowledge  «)f  homon  by  means  of  helera;  but  our 
knowledge  of  similia  and  of  differentia  is  not  predicated  upon  hetera   alone, 


28 
but  upon  siinilical  and  ditferential  relations  of  gregaria;  and  if  we  can  deal 
with  these  gregaria  so  as  to  discover  the  laws  of  causation  by  which  they  act, 
v,«  will  have  to  enter  nature's  mysteries  in  this  regard  by  getting  hold  of  re- 
lations existing  inter  gregaria.  Now,  nature  is  more  accessible  iu  some 
points  than  others,  and  her  relations  of  quantities  are  most  easily  compre- 
hentled  by  us;  we  will,  therefore  commence  to  evolve  the  laws  of  gregaria 
by  investigating  their  quautitive  relations.  But  for  this  purpose  we  need 
denominate  numbers,  which  have  an  homonical  standard  of  measure;  and 
space  is  the  only  thing  from  which  we  can  gain  such  denominate  and 
homonical  unii.  We  will,  therefore,  treat  briefly  of  the  denominate  unit  In 
this  chapter. 

If  the  hand  of  a  clock,  when  it  ticks  once,  posses  from  a  to  b  (Fig.  1.) 

in  the  small  circle  of  the  diagram,  while  a  body 
on  the  larger  circle  passes  from  c  to  d,  we  may 
take  the  well  known  equation  in  natural 
philosophy  S 


t: 


V  = 


T 


in  which  relations  the  space  from  a  to  b  may   be 

made   the    denominate   and    homonical    unit    of 

measure;  and  if  this  unit  will  apply  twice  to  the 

space  from  c  to  d  then  2 

.      V=  — =  2. 
1 

The  space  from  a  to  b  may  be  made  also  the  homonical  unit  of  measure  for  a 

steelyard,  a  barometer,  a  thcrmomeler,  steamguage,  momentum,  dry  measure, 

I'quid  measure,  money  and  throughout  nature. 

Then  let  V  stand  for  velocity,  S  for  space,  T  for  ttme,  W  for  weight,  and 

M  for  momentum,  and  take  the  following  equations  in  natural  philosophy: 

6. 


1. 


o 


3. 


4. 


5. 


8 


VW 


M 

V  =  — 

W 


S  M 

V  =  —        f^  -  VT       T  =  —       W  =  —       M 
T  V  V 

Now  if  Y  in  equations  1,  2  and  3  be  equal  to  V  in  equations  4,  5  and  6 
as  it  may  be,  and  we  take  the  value  of  V  as  given  in  equation  6  and  put  it 
for  V  inequations  1,  2  and  3;  and  we  take  the  value  of  V  as  given  in  equa- 
tion 1  and  put  it  for  V  in  equations  4,  5  and  6,  we  jvill  have  the  following 
equations: 

7.  8.  9.  10.  11.  12. 

MT            SW              MT             aw        8      M 
8  = T  = W=— ^    M  = —  =  — 


M     S 


W     T 


W 


M 


S 


w 


iSi 


29 

Gravity,  in  »  body  above  the  cartli's  surface,  is  noLhin-  else  tban   the 
tendency  of  the  aggregation  (o  fall  to  the  earth,  and  the  quantum  of  spare 
occupied  by  incommensural  a-grogal ions  inter  se  .iniilical,  Avhich  is  fourd 
by  multiplying  together  their  lengths,  breadths  and  thickness,  is  in   propor 
tion  to  the  quantum  to  this  tendency  to  fuH.    If  we  take  two  pieces  of  lead 
inter  se  sim.l.cal,  but  occupying  inco.nmensural  spaces,  the  piece  occupvin- 
the  greater  quantum  of  space  at  commensural  distances  from  the  earth's 
center  of  ^^ravity  will  possess  a  greater  quantity  of  gravity  than  the  other. 
Now  by  experiments  it  has  been  ascertained,  that  gravity  above  the  earth's 
sur  ace,  vanes  inversely  as  the  square  of  the  distance  from  the  eartli's  center 
or  direct  y  as  the  ratios  obtained  by  dividing  the  square  of  the  radius  by  the 
square  of  the  distance  from  the  eartli's  center  to  the  body  above   the  earth's 
surface.    And  hence  let  G  stand  for  gravity,  r  for  radius,  Q  for  .luantity  of 
matter  and  ^  for  the  distance  of  the  body  from  thoearth's  center,  and  *ve  will 
have  the  following  equations: 


G- 


13. 
Qr^ 

82 


14. 


15. 


Q  = 


S^G 


S2= 


I " 


^0w  If  S  in  equations  1,  2  and  0,  be  equal  to  S  in  equations  l:J.  14  and 
la,  as  It  may  bo,  and  we  substitute  the  value  of  S  as  ijiveu  in  equation  2  for  S 

m  equations  l;U4  and  15,  and  the  value  ef  S  as  given   in   equati<m    15    into 
equations  1.  2  and  3  we  will  have  : 


16. 


G-r 


Qr2 


10. 


IT. 

V2T2G 

Q- 

r« 


20. 


18. 


V.T2^ 


G 


21. 


8  =  RT\  /^ 

V     G 


Now  what  is  called  the  snecifie  n-mvifir  ^r  ^     i- 
SravUies  between  a  certain  qurtl  ;orjro     iriocra":  """'""  1 
quantity  of  ditferential  substances  as  measured  Z  !  commensural 

the  ratio  obtained  by  dividing  the  a  avhv  ^f  ^  ^T'  """'  """''"'-"  "' 
gravity  of  a  oommen/ura,  c,uantit  "o^- C.^^,"  ,;  ^Z  ^0^  n"!  '/'" 
the  commensural  quantity  of  any  subsfmcc  lZ„  ^  *""''   '*"■ 

of  water  equal  to  Q,  and  G  for  .L  "Sr^f  o  [„  ^'T'^  "'  '"'""""'y 
water  and  S  for  ,.eci«c  .ravity.  and  ^I'l^iirhll'^b.-^rL^-^S:;!'- 


30 


oo 


S=r 


G 


I 


And  i(  G  in  e(juation  22  equal  G  in  ec|uaiion  Ifi.  and  we  subsiituJe    we 
will   hav»':  (^r^»l 

An<l  in  ail  lh'»  Inregoing  fqnatioi.s  ihc  slaiulard  nt'  in<'asure   is  a  (h-nominnte 
and  li<)in<'ni''ai  unit  of  s]).i(-('. 

flT.MTKK  X. 

ItATM).  ' 

ir  on*'  of  two  numbe!s  he  mad"  tlie  numerator  and  the  other  dcnomi- 
iiatfM"  of  M  rfinmon  fraction,  the  ratio  of  ilie  nnmerjUor  to  tin?  d<Mu»niinalor 
is  vuel\  muniHT.  that  it  von  nuiltinlv  t!ie  den'-niinator  bv  it  you  will  l»ave  tlic 
nunieraW)!,  and  if  yon  divich*  tin*  minu-rator  liv  i'  yon  will  hnvc  tin*  denonji- 
luiioi  :  and  the  raiio  of  lUr  denominator  lo  the  numerator  is  such  numl)e;-, 
that  if  you  mnlliply  the  nunieraior  by  it  yon  will  have  the  deiioininHtor,  :m(i 
if  yon  divide  the  d»'nonHn:»tor  by  it  yon  will  li.we  the  numerator;  and  as  liie 
ratio  of  two  numbers  generally  ap.pears  in  tiu'  form  <»f  a  iVacJon,  (w  hich 
how.'ver,  n\ay  sonjetinies  be  a  whole  numbe!)  when  yon  have  tin?  ratio  of  the 
nnmeiiifoi-  to  the  denominator,  IT  yon  iiiveji  liie  !erms  of  ilie  Iractio'i,  you 
will  have  ihe  rn'io  of  the  denon;inator  lo  the  numerator,  ami  vice  versa, 
Xow  ail  persons,  vviio  have  studied  inathemalies,  will  understand  tiie  follow- 
ing j.roposiiions: 

!)  a  M  ^  oc  0  « 

;i     .)     0.    —=0.    —-a.   —---0.    —=1.    — =00.    —-=0.     -j:XOr=l.   and    — =1. 
a  0  '^  <»  0  ^  0 


In  these  propositions  zero  or  0,  is  to  be  nn»ler»to(»d  as  meaning  nn  infinitesi- 
mal <|U:intiiy,  i.  e.,  a  (|nantify  h-ss  than  anr  assignableqnantity  and  x  is  its 
reciprocal. 

Now  none  of  the  foregoinir  propcv^iiicms,  excejUing  Ihe  last  one,  need 
any  explatiation  for  the  mtitlH-malitians;  the  symbol  0 

•  0 

liowever,  needs  some  explanation  as  the  nnwhematieal  treatises  used  in  our 
scho<ds  and  colleges  have  not  given  to  it  its  true  siiinificanee,  which  we  will 
now  prcK-eed  lo  explain.     Take  the  |)roposition 

a-J— b-" 

1.  Xrr 

a'-i— h2 
If  in  this  eqtiotion  we  make  a  — b,  we  will  have 

0 
3.  x= — — 1.  ^ 

0  • 

But  in  equation  1  the  numerator  is  a  multiple  of  a — b,  and  it  may  be 
]>nt  into  the  fcu'm  of  (a — b)  (a'-i-f-'ib-f-b-);  arid  the  denominator  is  also  a 
multiple  of  (a — b),  and  il  mfy  be  put  into  the  form  ot  (a — b)  (a-i-b).  and  then 
ue  will  have 


i 


SI 


:3. 


X- X 


(a— b)        («-|-l»; 
Now  from  this  equation  we  inny  liavc 

0     (a5i-fab+i.^)      0Xa--fOX»»b-f-'>xl»'2     0 

4.  x=— X =: -  — -1. 

0  (a+b)  (OXa-f-OxlO  0 

Or  we  niav  have 

•'     0      (a-«i-|-ah-fl)5J)  (a2-f;i!,-fi,.)     a,,'^    ;^m 

•     0  (a-i-b)  •>  (a-fb)  2a       2 

How  are  those  iucoiiunensural  results  lo  be  explained  r    Now  as 

0 

0 
1  is  the  raiio  of  the  numerator  lo  the  denc.minalor  and  also  of    the   (lei.omi- 
nator  to  the  numerator,  as  ii  always  is  when  tlie  numerator  and  denominaior 
ure  absolutely  eummen.Nura;    thus  0  4         8 

—  =  1,— =1,— —  1,  etc. 
0  4  8 

And  it  iseviden:  that  in  ecuialion  4  we  have  taken  the  fVaetinn 


a-hb 
and  mnliij)lie<l  iis  numerator  and  d(  nnnnnaiMi-  by  (he   conuDon    inrinitesmal 
quantity  a 

while  in  equation  3  we   have  mnliij)iie<l   the  j^ame  fiaclinn  by  the    raiio   ..I' 

a  a 

—  to  — 

cao        oc    . 

i.  0.,  by  the  nitio  of  commensural  quantities.  Xow  it  is  eviden:  that  when 
the  numerator  and  denominator  of  a  fraction  are  eomuiensura,  their  ratio 
Will  be  the  denominate  unit,  and  it  is  als(»»evhlent  that,  i!i  all  proper  fraelions 
the  ralH)  ot  tne  numerator  to  the  demmiinator  will  be  h-s>  than  the  dent.mi- 
nateunit:  it  is  ai.u.  evident  thai  the  rtifterenci'  between  i.  «i>d  i ,  will  be  a 
jrreater  quantity  with  refeience  to  the  denominate  unit,  than  the  diffeienee 
between  t^  and  N,  while  their  raii«>s  a»e  eommen^ura:  thus  ^-:-  i,  =  i^  and 

^"^;'-^'7^!J"'"-"'^^'  t>»^^2-^-;ll  and  1^-1^  =  ;^  and  l/Vi^.  "And  the 
greater  the  decrease  ol  the  numerator  and  den.innnalor,  while  their  ratios 
Temainc.mim^nsuia.the  le^s  wdl  be  their  (lirtere;:ee  in  nnnierieal  value  com- 
pared with  the  denominate  unit;  and  hence  the  dilference  between  the 
numerator  and  den(»minator  mav  become  infinitesmal  and  the  ratio  all  tlie 
time  remain  the  same,  i.  e.,0-0<0,  while  0-0=1,  results,  which  can  only  be 
true  or  infinitesmal  quantities  in  their  relations  to  our  minds.  And  if  bv  0 
we  mean  ah^.Iutely  nothing:  at  all,  0^0  is  nothing,  0-0  is  nothino-  at>d  0x0 
IS  nothing;  and  it  by  oc  we  mean  something  without  limit,  aX  od  is  not 
within  our  conceptions,  nor  is  oc-  oc.  Jiuf  although  we  can  not  conceive  of 
absolute  existences,  and  of  course  can  not  deal  with  them  intellieently  vet 
we  can  conceive  ot  finite  relations  as  beintr  absolutely  commensural  and  in- 
commensural   and   hence  if  we  have  equation  4  or  ",  a>  rdiove,  we  mav  con- 


33 

ceive  of  (he  r  lationsof  a  — b  in  the  numerator  and  in  the  denominator  as 
absolutely  commensinal,  and  of  a  and  b  as  ab-*(dutely  c<»mmensura,  and  then 
the  relations  contained  in  a— h 


a-b 
will  de^lroy  each  otlu-r  and  this  fratrlion  will  liave  no  relation  t«»  otlVr  towards 
the  other  factor,  i.  e.,  its  refations  will  be  a  nonentity  and  it  need  not  be  con- 
sidered, but  if  a  — b  in  the  ilenominaror  be  an  intiuitesmal  quanity  and   a— b 
in  llie  uumeral<»r  b**  an  absolutelv  co-umensural  nifinilesu»al  (luanlity, 

a-b 

a-b 
will  absolutely  equal  1,  tlie  denominate  unit ;  and  we  have  seen  in  the  pre- 
vior.s  chapter,  that  the  denominate  unit  is  the  space  which  is  the  homonical 
standard  lor  the  measurement  of  lime.  Now  wlif-never  any  numi>er  is  mul- 
tiplied by  1  the  number  is  laken  one  lime,  i.  ^.,  ii.«>  value  is  not  afteclid;  and 
wlieiiever  a  number  is  multiplied  by  al)so;u!ely  nothini:,  i.  <•.,  not  touched  ar 
!Ul,  its  value  is  not  aff.'Cled;  and  he  .ci'  any  n'lmber  multiplied  by  absoIu;<'iy 
nothin:;  will  rcmai;i  In  tlic  same  relations,  as  when  il  is  multiplied  by  liie 
I  .lio  nf  twf)  numbers,  uhysc  ditt'crence  is  alisolutely  nothing;  and  tlufrefore 
in  equaii<»n  4  w«-  lauitiplieci  both  numt-ra'or  and  denom.iia'oi  by  an  infini- 
u'smai  quanlit\ ,  which  prodnred  product-;  whose  diffeienee  was  not  al^o- 
Intely  noihinij  thonirh  taken  t'»  be  so,  while  in  equation  5  w  multiplied  by 
the  r-.'i«»  wf  two  numbei>,  wh.)se  ^.lifierence  was  ab^oluiely  noihing,  and  iience 
the  incommen-nial  resul'.s.  And  -loon  the  ^up{>osi:ion  wiih  wliici'  wolarted, 
i.  e.,  iii:il  a  was  absolutely  ecjUal  to  li,  ((piaiion  ,")  rontains  liie  Hue  p'suit. 

Now  from  the  the  t'orogoing  discus.siim  it  vvil'  appear  that,  ihesymlxd 
niay  be  made  to  make  its  appearance  in  every  ratio  by  factoring  and  sup- 
jjosing  the  ditiereiice  between  ihe  numeraior  and  denon»ina>or  <»*    one  of 
the  factors  to  he  le.ss  lUan  any  t-ssii;;nable  quantity:   llius  the    ratio   of  4 
is  V,.  which  may  be  etpial  to     a 


0 
0 


—  vi 


b 


X 


.  -2' 


when  the  ditVerence  between  a  i»nd  b  is  less  than  any  assignal»le  (|Uantity  and 
we  multiply  bv  iheir  ratio;  but  if  we  multiply  by  flu'  quantities  themstlves 
we  wiii  hiive  0 

0  4 

i.e.,  we  will   l.ave   1    instead  of  i.>.     To    iliusirate  bv    fio;ures    let    i/g-— X^ 

4 
and  if'  4—4  abs(dut«ly  and  we  multiply  by  their  ratio  we  will  have  H  —  ^Xhz 
~}2^  or  if    we  mulliplv  in,  we  will  have  4X1      4 

4X2     8 
but  if  4'a!id  4  be  reduced  to  infinitesimilly  small  quantities  and  we  muhiply 
in  we  will  ha^'e  0  ' 

^l. 


H' 


we  will  have 


0  or  if  4  and  i  be  made  enormously  large  quantities 


}o' 


= =1.  0 

*  And  hence  the  symbol    — 

0 


.    as 

lesiuais.  aiul      ^^- 

X     is  Its  rociprocal;  i\m\   tlic  nilio  of   llif'y(M-a(i(.s  is  1  •  lims 

—  -^  —-=1  Mild  —  -^  —^-1. 

i.  e.,  tjjf  iriiio  of  ratios,  wliich  :uo  reoiprocail.  is  nhf.ivs  flK-  .!(noinn.:!i('  in.ii  • 
and  luMicc  the  iruc  slirnificancc  o[     (»  ^^ 

—  and -- 

'*  ''     i^  i:Ui.)  of  if(;i|»roca|  ratios, 

•li"  wo  take  the  <Hjiiali(iii        a-— Ir-^ 

(J.  X:^  

0  (a— b):^     .'ind  make  a-.  !>  iiiiiiiit(-iiP.allv    wf 

will  have         4.         x=— =-l ; 

<>  l>i»f  l>y  taclorino-  a.'jcJ  cunt'cHin:::  \\r  wiji  haw 


8. 


a-fl)    a  — b    H-|-b    *J:i 


X— X 


= — ■-•--■  -/:. 


i\  —  b    a  — b    a—b      0 
Now  if  by  0  \\v  mean  al»solulily  uoihiui,'  th<'M  \=''2:\   and 
X     2st  2a 

— =-  .  i.  c,  —  wil!   be  the  true  ratio  of  x  to  1 ;  and  if  by  0  we  mean   an   ih- 
111  X 

tinilesmal  quantity  ii»en  x-=  a  and  — =— ,  i.  p.,  -?  will  be  ih.-  true  ratio  of  x 

111 
to  1;  but  tlie  two  values  of  x  are  inconinieMsura,  L  e.,  in    the  fust  rase    it    is 
finite  and   m^  tlie  seooml  il  is    intinite:    and    we    wjll    haw    tl-e   proposition 

(a  — b)- 
10.  x= and  by  inakin<;  a=-b  inlinitesiinallv  we  will 

^^^"^'^  ^^-  x=— ,  this  last  equation  may  be  bialed  tiius  — «=— 

3a2  X      V, 


I 


•<   ■> 

•».4 


:5i 


and  if  by  0  we  mean   absolulejy  nolhinir  we  wili  liavc  — _— ,  i.  ...^  _  ^vill  be 

X       1  1 

llie  true  ratio  of  1  to  x,  and  if  by  0  we  mean  an  iufinilesmal  liieii    x=-0  and 

we  will  liave  —:=.—  ;  but  the  two  values  of  x  are  incommensura,  i  e    ia   the 
X      0  ,        ,  - 

first  rase  il  is  finite  and  in  tne  second  it  is    iniinilesmnl :  ar.d    we    will    hav<- 

tlie    proportion       X:l::0:1,    xXl=^Xl=0.      And    from   the   above   we  see 


0 


1 


1 


that  — ,  or  — -,  or  — ,  or  — ,  may    be  a  ratio  and  may  liave  a  ratio.    And    we 


1 


a      (X  0       0  X        0 

iiiayhave—-,  and -=-;  and  henee  —  or  —  may   be  a   ratio   and    may 

liave  a  ratio,  and  they  and  their  ratios  are  the  reciprocals  of  each  o;i>er 

^ow  the  whrde  oljject  of  differential  calculu^j  is  to  determine  the  ratio 
01  rates,  i.  e.,  to  determine  the  ratio  of  ratios;  for  rale  and  ratio,  when  applied 
tomouoQor  mei(M.se,  arethesamethinj;.     And  the    ratio    ol'   nno   eonsiant 


b 


34 

number  to  another  is  easily  found  by  the  ordinary  principles  ol  Arithmetic; 
it  is  easy  also  to  find  the  ratio  of  rales  of  the  moveiuents  of  two  bodies,  when 
their  rates  are  uniform,  i  e.,  when  each  one  for  itself  makes  commensural 
spaces  in  commensural  limes;  but  when  the  rate  of  one  is  uniform  and  the 
rate  of  the  other  |)roceeds  upon  some  law  other  than  Hiat  of  uniformity,  i.  e. 
when  it  does  not  make  commensural  spaces  in  commensural  times,  a  case  is 
j>resenied  for  the  difierential  calculus.  Let  us  then  examine  the  f^)llowing 
Theorem  in  the  calculus:  "The  rate  of  variation  of  the  side  of  a  square  is 
to  that  of  its  area,  in  the  ratio  of  unity  to  twice  the  side  ot  the  square." 
This  is  the  enunciation  of  the  Theorem  as  given  by  Prof.  Loom  is;  as  we 
consider,  however,  lliat  this  enunciation  is  incorrect  and  does  not  set  out 
(drarly  ihe  matter  to  be  proven,  we  will  irive  the  followin«^  in  its  stead:  The 
rate  of  variation  «)f  the  side  of  a  scjuare  is  to  the  rate  (»f  variatiwn  «»f  the  cor- 
risponding  area,  in  the  ratio  of  unity  to  twice  the  side  of  the  unvaried  square 

-|-  the  variation  of  the  side.  Let  a.b.  (Fi;r.  L)  be 
e Fi^rure  1.  f      tjie  side  oi  the  s((nare  a,  b,  c,  d  and    a,  and  sup[)ose 

jl^.^  ^.^j^^  j^^  ^^  elouiiated  to  e  in  one  second  of  lime, 

b  e  will  then  be  its   increase  and  the  corresponding;: 
increase  of  area  will  be  the  space  l»,  e,  f,   «r,  d,  c,    b: 
c  let  h=b  e,  and  g=bef«j:dcb,  then    h==increase  of  the 

side,  and  .i:=th('  corresponding:  increase  of  area. 
Now  ash  =  the  increase  of  the  side  in  one  .second, 
III*'  rate  f»f  this  increase  will 

h 
be  =-  — 
a  d  fT  I 

and  as  ^  =  lhe  correvpondinir  increase   of    area,   its 
r:\le  of  inerea>('  will 

iS                                                                   11        g        h 
be  =-.  —  ;  and  the  ratio  of  these  rates  will  be -. =  — . 

1  1        1         ff 

Now  let  X  =  ab— Ihe  side  of  the  s(piare  abcda,  and  y  =  ae— the  side   of  the 
square  aefira ;  then  y  — x  =  h,  and  yi— x-=g,  and  consequently, 

h       y— X       y  — X  1  1 

^r      y'Z-x'i      y-x         y-fx        y+x 

But  v-fx^2x-}-h,  and  tlKMefore: 

h          1 
11.        — = . 

g     2x+h 
15ut  as  the  value  of  ^  depends  upon  the  value  of  h,  if  we  make  h  an   infini- 
lesimal  (and  we  have  seen  in  2>J  that  the  ratio  of  infinitesimals  is  the  same  as 
the  ratio  of  appreciable  qnuatities  sprini|:in5   from  them  by  multiplication) 
we  will  have: 

0         1 
12         = . 

0      2x-f0* 
and  hence  for  infinitesimal  viiilations  we  have: 

b:g::l:2x. 

Note. To  treat  specially  of  mathematics  is  not  our  object  in  this 

work,  nor  do  we  wi.sh  by  criticising  to  offer  refutations:    but  as  the  under- 


III 


35 

standing  of  ratio  is  imp<>itant   and  as  ih,.  calculus  treats  spcciallv  of    this 

Sn  '  a'"'!  r  "'''n  ""'?''  ""f  ""''  foundations  must  be  acceptable  to  every 
Slue  ent  Ana  from  the  above  demonstraiion  it  will  appear  to  everv  refleclin- 
reatier  tliat  the  ideas  entertained  bv  many  teachers  i,r  the  calculu*^  that  h-" 
IS  not  the  true  ratio  of 'die  race  r>f  increase  ..f  ihe  side  of  a  square 'to  the  rale 
<»t  increase  of  tnecorrespondinir  area,  but  that  in  order  to  Lret  at  the  true 
ratio  we  must  reduce  h  and  or  to  infinitesimal  quantities,  so  .hat  their  difer- 
r'?H!'/vv?iVK;r /'•''"  •^"y  assignable  (|Uanlily,  supposinir  that  thereb/the 
moneoi^^  '"'''*''   '''  '""""  ^'*"'  "'*'^"  '''''>'  ^^•^■^*.^'»^Ht>l<'  M".->ntity,  i. 

.  Acrain   lake  the  Theorem:     The  rale  of  variath.u  of  the    d-M-  of  a  cube 

s  to  llie  rate  of  vaiiatnm  of  the  correspond  in":  .solidity,  in  the  ralio  of  unilv 
to  the  square  .>f   the  varied  edge -^  ihe  prndnc^t  of    the   varied   and   in  vn  ie  | 
edges  +  the  square  of  the  unvaried  edge.     Let  h  =  th«  variation  of  ed" e   an 
corresponding  variation  of  solidity;    and    !el   v -_- ed.ro  of   vari(nr  n      ' 
x  =  edgeol  unvaried  cube;  then  '  ' 


36 


or 

and  X 


h 
la.       — : 


V  — X 


g     y3-x3  ya-f-yx-f  x-^ 

If  within  this  equation  y=x  to   wMhin   less  than   a:)v  asM-nable  dillerence 
1.  nnd  g  will  become  infinitesi.nals  and  we  will  have  ' 

0        1 

14.  — = : 

0     :Jx-* 

and  hence  for  infinitesimal   variations    h -cr. .  i  .-u-'       ir  ii.,.  ,  j      i      i 

;„.,:.    ,      1     .•  •  •••.»i    t  ai  lai  luny,  II .  LT:  :  1  :o\'.       11    t hc  (M  (^C' be  decrcas - 

ingiusfeadof   increasing  x>y  anfl  we  will  have  'Micas 


1 


_      -»>        >:-}'  ■    -h 

^•*         —  = ' — ,  and  when  x  — v  — 

— g      \3-y8  _jr      yxii 


When  the  motion  or  variation  of  one  bodv  or  thin-  is  unif,  rm  ind 
another  body  or  thing  makes  commensural  increments  of  Vncrease  idecn'  t"^^^ 
<d  variation  in  consecutive  commensural  time>,  the  1  Mter  bmh  or  iV.i nl- 
vanes  in  Arithmetrical  progression;  and  in  order  iV^ehtio,  ? 
ratios  of  the  variations  we  must  divide  the  ratio  of  spacVma  le  bv  tl  e  fl is 
object  in  a  given  l.me  by  the  rati,  of  the  space  made  bv  ihc  sicond  o  jecf  n 
aeonmensural  time.     Let    h  =  space  made    in  five   ininutA   b      a    ''ob  ee 

five  min   iL  wi'tirjhe  e  ^^+'  '""  '"f ----''  ''+2d  for  thi  ihinl  and  so  o n>or 
cessive  mi^^^^^^^^^  commensural  increment  of  increase  of  .1   i„  .,,!.  suc- 

h 

then  -  =  ratio  of  the  first  objects  variation,  and  letting  S  stand  for  the  sum 

of  the  terms  iiUhe  second  objects  variation,  -^   .-.   ratio   of  second   object' 
variation  and  ~  =  ratio  of  these  ratios.     IJut''  letting  n  =  number  of    term. 

Md  1  =  last  term,  aiul  h  will  be  e,,,ml  u.  I,„,  an.l   1-=:  |  —  I  „    ,,.,.|   honce- 

l    8    J    ' 


s. 


bn 


2b 


IT). 


S      fa+l  ]        a-hl 

I In 

I     3     j 
ii  2b 


Hut  l=a-!-(u  — l)d,  and  hence; 


1«.        — = 


-,  and  when  n  — 1 


17. 

0      b 
18.        — =— 


h      b 

— rr — .  and  if  we  rediuje  h  and  S  to  intiniiesimals, 

8      a 

b 

— ,  ilierefore,  is  the  true  ratio  of  the  objecis'  variations 
•0       a        a 
at  the  infinitesimal  poinl  from  which  they  Degin  to  v;;iy. 

a  a 

The  cipiation  — = irives  the  ratio  of   Ihe  first  term  in  an  Arilh- 

1       a-Hn-l)d 
metrical  progression  to  the  last   term  cons'der-.'d.     If  the  reader  does  no 
fully  comprehend  this  and    the  follownig  paragraplis,  let  him    lUrn   to   some 
mathematical  work  uj)on  Mie  subjejts. 

If  oiie  «d)Ject  vary  uiMfoimly  and  another  obXect  vary  in  such  manner 
that  the  successive  values  made  in  commensural  times  are  in  proportion  to 
each  other,  i.  e.,  the  lern^s  have  a  «:onsiant  rati'),  the  latter  object's  variations 
are  in  (Jeonutrical  piogiessioii ;  ami  we  find  the  ratio  of  these  object^■,'  vari- 
ations by  dividing  the  raiio  wf  the  one  by  the  ratio  of  the  other.  Using  the 
letters  as  in  the  |)receding  paragraph  with  the  addition  of  r  for  the  constant 
ratio,  and  relying  upon  the  leatlers  knowledge  of  mathematics  we  will    have: 

h        bn        bn('-l) 

20         — — — .      Hut  when  i>.=-1  we  will  have 

S     ai»  — a      a(r»  — 1) 


/W  1  • 


r-1 

h       b  l» 

—  =  — ,  and  conse(|Ueiitly  —  will   be  the  U'ue   ratio   of   these 

S       a  .     H 

objects'  variations  at  the  zero  point  Oi  varying.      The  equation 

a          a 
'22.    —  = gives  the  ra'io  o."  .he  first  teim  to  the  last  term  considered. 

1       ar»— 1 
If  an  object  varp  in  Ariih-net'-ical    p-ogressio  i  and  another  by   Geo- 
metrical progression  and  we  use  cap'   d  lei  eis  i.i  the  Geome  lical  equation 
for  th«  sum  and  first  'erm  we  wl|  have 

I  ••+>  1 
;  I  n 

s        [21      |r(a-;-l)-(a+b)]H 
S       l.—A  2(lr— A) 


r— 1 


37 
We  have  gone  far  enough,  perhaps,  up  ,n  the  suh.ject  <,f  ratio 

CHAPTER  XL 

TKANSFOKMATfON   OF   I'R(HM)s[TFONS. 

If  we  take  tlie  three  (list. net  proposilions- 

A 
I. 


A  V    A  A 
'^  S   T  S    T  S 


A  A    A  V    A  A 
TS    TS    TS 


A  A    A  V    A  A 
TS    TS    TS 


<l 


H 


—  <t 


ft  <  I)  c  < 

by  uniting  iheni  into  one  we  may  have 

A V      A V      AV 

TS     TS      TS 

3. 

ft       <  ;:      b 

c  (i 

And  if  in  proposition  2.  we  place  the  siirn  a  or  V  bv  the  ^i.h.  mF  n  .    . 

not  as  signs  of  homon  or  jje  era   bni  simi  Iv  ul  iU^  •       **";'  ."^  *'"*  ''''"^ 

we  will  have                         "t-'t^r.i,  one  MmpJ^  as   the  sign   ot     ineonnncn>ura 

A  ^      A  V      \  \ 

T  8     T  S       r  s 


•> 

o. 


Via     < 


i  *■ 
ir  we  lake  the  distinef  propositions 


4. 


A  A     A  \      \  A 
T  S     T  S     T  S 


T  S      l\s      T  S 


A  A      A  V 
T  S       i'  S 


A   V 

r  S 


c 


ii 


—         i\ 


•^         <  b  b        ==. 

by  uniting  them  into  one  we  may  have 

A  V  A  \ 

TS  AV  TS 

•». TS 

A  jft  =■■  bj   . 

«    II   -    ^s         ^     n-     ...      .^^ 

,         ^  ^ .  7. T  S 

.ij-_c    ==-<     b+d  axe      ==<    bxd 


A  V       ^  V     A  V 
T  S      T  S      T  S 


A 


<  >  <  T 

If  we  take  the  commensural  propositions 

t^         ,,      A  A 
TS     ^^  V     TS 

»• TS     


a 

V. 


<     b 
d 


V 


T^      AV      is? 


A  A  \  A 

TS  ^   V  fh 

T  S , 

a  —        d 


by  using  „.e  .„,„  Of  eonunensura  ,„„nha.  „f  «!„,„,)   I,,  „.-„,';.,   ,„^. 


terms  wc;  may  liave 

A    ^'       ,\    *        AV 
TS       TS       TS 
10. ,  from  which  we  may  have     11. 

II  1ft      ==     b!  „ 
d     " 


c 


A  V 
TS 


A  V 
TS 


AV 
TS 


12. 


axe       ==       bxd 


and 


A  V 
TS 
13. 


A  V 

TS 

a-j-c 


AV 
TS 


A  V 
TS 


88 


A  V 
TS 


=     b+d 


AV 
TS 


II 


a 


e 


=  =      b 
d 


If  we  have  any  number  of  incommensural  propositions  as  the  follow- 


ing: 


AA  A  A 

T  S  A  V  T  S 

14. ^s  , 

n  <         b 

we  may  derive  from  them 


AA 
TS 

b 


A  A 
AV  TS 
T  S , 


< 


c 


A  A  A  A 

T  S  A  \"  T  S 

T  S ,  etc. 

c    <  d 


A  V    A  A   A  V 
T  S   T  S   T  S 


A  A 
TS 


a-fd 


A 


A  V 
T8 

a-f-d    aXd  A  < 


AV 
TS 

aXd 


AV 
TS 

17. 

a 


A  A 
TS 


AV 
TS 


a 
d 


A 


And  if  we  have  any  number  of    incommensural  propositions  as  the 
following: 


\  A  A  A 

TS  AV  TS 

18. TS  — - 

a  ^  b 

we  may  derive  from  them 


A  V 

TS 


19. 


'l^S      AV 

TS 

A  A 
TS 

d 

TS 
e 

aV 

TS 

< 

TS 

f 

A  .'X 

TS 

A  \- 

TS 

ptr» 

etc. 


a-fb+c+d+e-ff  a 
<  <        < 


a+b+c+d+e+f 


By  setting  down  all  the  signs  in  our  transformations,  we  are  able  to  integrate 
or  re.solve  the  complex  propositions  into  th«ir  simple  and  primitive  ones 
without  any  difficulty;  but  there  is  still  another  object  of  more  importance 
in  doing  so,  as  we  will  see  hereafter. 

Now  we  have  shown  hereiofore,  that  both  incommensural  and  com- 
mensural propositions  contain  only  relations  inter  se  similia,  and  as  we  have 
used  the  letters  a,  b,  c,  etc.,  not  to  distinguish  kinds  of  things,  but  merely  to 
distinguish  the  quantities  of  similia,  proposition  6  may  be  translormed  into 


39 


20. 


A  V 
TS 

a-fc 


TS 


out  the  sigus  of  equali,^  8o5  inenZtv  befwZ^l''  ''•'"»f<"-™^J  ''J'  "Hking 
their  stead  the  sign  of  similia^    ^        ^  between  the  terms  and  inserting  i° 

^imi.ia'l^n^  diff^J'nl^'S  tk^e  fhe';;;^^ tlafV^SnT''^''  '''^""«"''" 


21. 


and  

^         b  c 


AV 
TS 


oo 


Take  the  propositions 

Av 
TS 


TS 

d 

AV 
TS 

H-H- 


By  unitin.jr  them  we  will  have 


AV 
TS 


b 
fl 


23. 


TS 


H- 


24. 


%  unitinfT  we  will  have 


a 
b' 


AV 
TS 

II  H- 


A  V 
TS 

a' 
b 


^"  %iB^'S»-S^=;:-z,siu-' ■- 


2«. 


AV 
TS 

II 


TS 


A  A       A  V         A  A 

T  S     T  S     T  S 

~"r      ~~"    ~7;,     %  uniiinor  them  we  have 


07 


A  V 

TS 


A  V 

TS 


A  V 

TS 


' ' ' 


a        II  I! 

a"  a' 

depeud?u;or,i':ra!;7:ptr:l;:,i" ''':''''•;  •"^"''•'  <=«p»^"v  ->  '--ate 

a  single  remark  further  -  n   thkt    u  .  !•«  Y^r'i*"'!?''  ","  IT''"  *^"'"'k''  '"  >""ke 
hoih  see  the  bell  and  hear  its  i,  „„.   in  L  T    "     "•   ".  ''*^"   ''e  struck,  we  can 
cupies  an  h.,m,.nical  space    b«    the  or^a"^''';"'"'^"'  ''""";  "''"«  "'*  ''*"  <'c 
"ccupyheiericul  spaces;  and  t  e  sminj    "<'  ''  "'•"■"  "       """'  "*"  ^'^"""^ 
Uo  uot  come  to  .he''mind  throui^'^.  ^trVtc^Vriuh^o!.^!?' t.'.'i^e'^^'i 


40 
appiMeutly  in  the  case  homonic&l  time  and  spaces  yet  the  spaces  are  really 
hetera,  and  they  eaable  the  mind  to  heterate.    Take  the  hetcrical  propositions 

r/^A  A^  AA 

T  S      T  S     T  S 

.      By  uniting  them  we  will  have 

b         A         b' 


28. 

a 


A  A       A  V       A  A 

TS     TS«   TS 


a' 


29. 


T  S     T 


V     ^v 

S     TS 


VV 


a        VV        a' 
b  b' 

Bui  if  we  should  transpose  the  terms  of  the  first  of  propositions  28  and  then 
unite  it  with  itself  we  would  have 


30. 


aY,    aa 

TS     TS 


a 
a 


aV 


:n 


Take  ilie  propositions 

A  A       A  A       A  A 

T  s     r  S     T  s 


aV 

TS 


a 
a 


A  A 
TS 


rs    ^% 


a 


a 


b         A  b 

^4  n 


And  by  uniting  them  we  have 


32. 


A  A 
TS 


a 
b 


a 
b 


Hut  if  we  unite  the  first  of  the  propositions  81  with  itself  we  will  have 


^ 


33. 


A 
S 


a 
a 


aa 

TS 


AA 


AA 
TS 

.a 
a 


Now  from  the  few  examples  given  above  anv  one  with  moderate 
capacity  can  see  how  to  unite  and  transform  simple  propositions  into  com- 
plex ones  and  obtain  all  the  varieties  of  propositions  having  the  varieties  of 
signs  between  the  terms  as  set  down  in  Chapter  First  ot  this  book  and  to 
place  the  appropriate  siijns  over  the  T's  and  S's,  we  need  not  therefore  deal 
lurther  with  this  matter. 

Now  we  have  seen  in  Hook  I,  that  in  every  case  of  causation  some 
homon  is  converted  into  hetera  or  vice  versa;  some  si m ilia  are  converted  into 
differentia  or  vice  versa;  or,  some  commensura  are  converted  into  incom- 
comensura  or  vice  ve  versa:  and  if  we  compare  the  simple  propositions  with 
the  complex  ones  derived  from  them  in  thu  proceeding  transformations,  on 
comparison  of  the  signs  of  the  S's  over  the  terms  we  will  see,  that  in  the 
transformations  given  the  heteration  of  space  has  occurred.  In  those  trans- 
formations of  propositions,  however,  the  heteration  of  space  mav  have  been 
made  merely  by  the  mind;    but  if   we  suppose  a,  b,  c,  etc.,  to' be  material 


41 

•  M  tlM-  toieir.Mnnr  comi.lex  i)n)posiri.,ns  re  be  causes  h.      llr  .-Vb    '  P'  '^^^•' 
•>t  lime  and  a  liomoo  ot  space  over  ihe  i.m.L   .m^\  "s  iMake  a  li..m(,n 


:;4. 


.'  A 


•A  A 
'J'S 


V         — 


We  ,„ny  ut-al  will,  ,,r„„„»i,iou,s  T  and  S  iu  a  similar  .uannc-r. 

lor  JiZ  w;«i;i  l,av,!"  •'  '""  ""■  """^  '"■  I""l"->i"u  H  and  1..,  vs.an.l 

f^      l\s      fj; 


:{.">. 


Ami  if  in  this  proposition  we  d 
have 


•anire    \   jnio   \  between    Ihe  leinjs   we   will 


A  A 


ao. 


TS 


AA 


must  lifpnSr  and  ^  :::'.T^:'  'V^  ^ ''^^\   '»-^^^"-   ^-   effects 
inter  se  nu,st  he  differentia      C^^  clifte.entia   the  effects 

other,  and  we  will  have  ''  ""^  "*   '"^  ''^'''^'  '»"*»  >•  f"'"  "»« 


37. 


A^       A  •        A  A 

T  8     r  s     r  s 

X  H-  y     ' 


io^/r;^:Lte„)i'  ;?'°e:  ^::zz^--^  -  ^^"' "-  •• 


m  effect  diff'er- 


4% 

AA       AA       AA 
TS     TS     TS 

38. . 

z         A  z 

Let  us  now  take  propositions  23  and  go  through  all  the  transforma- 
lioDB,  which  the  reader  will  now  readily  understand 


a' 

H- 

b' 

U 

TS 

a 
b' 

II  H- 

aV 
TS 

a' 

b 

U 

H 


a 

b' 


^l 


1!  H- 


TS 


X 

II 

X 

n 

A  A 
TS 

A  A 
TS 

A  A 
TS 

X 

A 

X 

2X 

AA 
TS 

AV 

TS 

AA 
TS 

X 

II 

X 

U 

AV      AV      AV 
TS      TS     TS 


a' 
b 


Produce  by  heterating  space    between 
objects  in  terms  towards  each  other. 


By  homouating  space  between  objects 
in  terms. 


By  homenating  space  between  terms. 


By  heterating  space  between  terms. 


By  heterating  space  between  objects  of 
terms. 


^ 


AA 
TS 

a 

A  A 
TS 

a 


A  V 
TS 

H- 

A  V 

H- 


Icrni 


•  Jieteialin^r  space  bolween  oJ»iecK  o( 


TS 


h 

A  A 
TS 


!»' 


'■-H.e,.  z  i'::;:r  :„:;l  '.".rr;:;  r;  "-^^  --' -" ""» -"^ <- 

coml,i„a,i„„s  in  l>.oposi,io^    ^  !\^    j ',,  v   ^^  ■«'-"  "f  frrcg..,!,.  and   of   U,ei,. 

c"..  >-evolvecl,,;poi,uou  errors  r  ,0  r  '"""'  """»"«  "»•  "■"""' 
l-""osop|,y,  to  „a,e  experh  .e  ,  s  „  adel^  "mlanu.nlal  principles  in  „„.,ral 
•-necl  in  iig,.,,  electric  ,y  an! itT  Bn  "7"."'^""'^'«  ''^-'"^  "«'"ally  ob- 
fmc.Uy  in  geuing  .„c  amlun.  1  f  p'r  ."'r' '"  """""•  '""^  '-^"-' 
fore  .he  scienlific  world,  have  com,  el  !,i  '         '  '"  "'  '"  '"'«=«  •''«'»  »>«- 

tl.e  subJecMs  abrnpllv  broken  offZm  '""    '"  ''"''  '"-"•''=    "'"'""«'' 

tl.e  science  ,o  the  invLi.a,,^„  „,  Z'ZT  '""T^'''  "'*  "PP'i^ability^f 
"'at  1.0  has  made  many  v;i  I  «  uiclve  i^  "  ?'"""-"*''  "'«  """'"^  «'"'»'* 
be  left  for  ano.her  work  and  ,r  Ze  ','  '"  "'"""'  ''='""'=^-  "■""^"  '""^t 
s<.ould  ever  come.  The  pres  n  Lui  n  ,.  f """'  '^"•'="'"^"'"«''«.  if  such 
l^arrisin,  circumstances 'and  1  ffie^„ri':  ""  '"  '""""  ""^-- •"<••  "-'t 
"tlierwise  than  that  numerous  eVror,   „  ,         """'"  '"'  ^'^l''^^^'^''   'o  be 

'n.e.se  the  reader  will  ex  ."e  «  dlh  n  "'"'"  ^""'"^  "W-"  ">  "• 
vesli„-ated  the  work  and  expres:ed.h,.i  '"'""'^''   "'^'"   ^''••'"    ''uve   io- 

bet-er  prepared  to  judge  :reM,;rr:t"''  "  ""^ '""'"•^  «'"  "« 
pie  e  a  work  on  natural  vmosoZtl^ Z,^^'"'  '  "  '""'"'P'  '"  «»■»- 
and  reasoning  exhibited  in  this  b.H,k  '  P'""^'l"<^^  "^  experimet:l 

TUI  KNU. 


J 


